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The percentage P of doctors who prescribe a certain new medicine is P(t) = 100(1-2-0.15), where...
0.24), where is the time, in months. Complete parts a) through d). The percentage P of...
0.24), where is the time, in months. Complete parts a) through d). The percentage P of doctors who prescribe a certain new medicine is P(1) - 100 (1 - a) Find P(1) and P(6). P(1) = % (Do not round until the final answer. Then round to the nearest percent as needed.) P(6)= % (Do not round until the final answer. Then round to the nearest percent as needed.) b) Find P' (t) P't- c) How many months will it...
*10. The size P of a certain insect population at time t (in days) obeys the...
*10. The size P of a certain insect population at time t (in days) obeys the function P(t) = 100 e 0.04 (a) Determine the number of insects at t=0 days. (b) What is the growth rate of the insect population? (c) What is the population after 10 days? (d) When will the insect population reach 140? (e) When will the insect population double? (a) What is the number of insects at t= 0 days? insects (b) What is the...
- A population grows at a rate P' (t) = 300t e where P(t) is the...
- A population grows at a rate P' (t) = 300t e where P(t) is the population after t months. a. Find a formula for the population size after t months, given that the population is 3000 at t=0. b. Use the answer from part a to find the size of the population after 7 months. a. Find a formula for the population size after t months, given that the population is 3000 at t=0. P(t) = (Type an exact...
an account at an interest rate r compounded conltinuously, then the amount A (caled the future value of P) in the a...
an account at an interest rate r compounded conltinuously, then the amount A (caled the future value of P) in the account t years from now wil be A P Solving the equation for P, we get PrAcft, In this formulation, Pis called the present value of the investment. (a) Find the present value of $400,000 at 6% compounded continuously for 25 years (b) Find the interest rate compounded continuously that is needed to have $40,000 be the present value...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the popu...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the population'? (b) At what time (i.e., after how many months) will the populaton be equal to one half of the limiting value in (a)? Do not round any numbers for this part. You work should be all symbolic.) Problem #6(a): 10000000000 Enter your answer symbolically,...
1 8t(2t - 1)(t + 5) Given p(t) answer the following (t + 5)(4 – t)(7t...
1 8t(2t - 1)(t + 5) Given p(t) answer the following (t + 5)(4 – t)(7t + 2) questions: Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. a) The domain of p in interval notation is: Interval Notation: b) The t-intercept(s) are: c) The vertical asymptotes of p are at t = Write the answer(s) as just numbers separated by commas. d) p has a hole at the ordered pair: Write each...
For a certain product, cost C and revenue R are given as follows, where x is...
For a certain product, cost C and revenue R are given as follows, where x is the number of units sold in hundreds. Cost: C2 = x2 + 102 VX +55 Revenue: 892(x - 5)2 + 25R2 = 16,900 dC a. Find the marginal cost dy at x = 5. The marginal cost is estimated to be $ (Do not round until the final answer. Then round to the nearest hundredth as needed.)
Find the savings plan balance after 6 months with an APR of 8% and monthly payments...
Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300. The balance is $ (Do not round until the final answer. Then round to the nearest cent as needed.) Enter your answer in the answer box and then click Check Answer. Clear All All parts showing O Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300. The balance is $1! (Do not round...
21² + 6 Ay The population, P, in thousands of a resort community is given 100...
21² + 6 Ay The population, P, in thousands of a resort community is given 100 600t by P(t) = t20, where t is time, in months. 80-A a) Find the population at t= 0, 1, 3, and 8 months. .60 b) Find the horizontal asymptote of the graph and determine the 401 value that P(t) approaches as t goes to co? c) Explain the meaning of the answer to part (b) in terms of the 20- application 0 10...
AY 150- A company's total cost, in millions of dollars, is given by C(t) = 90...
AY 150- A company's total cost, in millions of dollars, is given by C(t) = 90 - 40e - where t is the time in years since the start-up date. The graph of C(t) is shown to the right. Find each of the following. a) The marginal cost, C'(t) b) C'(0) c) C'(5) d) Find lim C(t) and lim C'(t). t00 100 75- 0- 0 15 30 a) C'(t)=(Do not include the $ symbol in your answer.) b) C'(O) =...
0.24), where is the time, in months. Complete parts a) through d). The percentage P of doctors who prescribe a certain new medicine is P(1) - 100 (1 - a) Find P(1) and P(6). P(1) = % (Do not round until the final answer. Then round to the nearest percent as needed.) P(6)= % (Do not round until the final answer. Then round to the nearest percent as needed.) b) Find P' (t) P't- c) How many months will it...
*10. The size P of a certain insect population at time t (in days) obeys the function P(t) = 100 e 0.04 (a) Determine the number of insects at t=0 days. (b) What is the growth rate of the insect population? (c) What is the population after 10 days? (d) When will the insect population reach 140? (e) When will the insect population double? (a) What is the number of insects at t= 0 days? insects (b) What is the...
- A population grows at a rate P' (t) = 300t e where P(t) is the population after t months. a. Find a formula for the population size after t months, given that the population is 3000 at t=0. b. Use the answer from part a to find the size of the population after 7 months. a. Find a formula for the population size after t months, given that the population is 3000 at t=0. P(t) = (Type an exact...
an account at an interest rate r compounded conltinuously, then the amount A (caled the future value of P) in the account t years from now wil be A P Solving the equation for P, we get PrAcft, In this formulation, Pis called the present value of the investment. (a) Find the present value of $400,000 at 6% compounded continuously for 25 years (b) Find the interest rate compounded continuously that is needed to have $40,000 be the present value...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the population'? (b) At what time (i.e., after how many months) will the populaton be equal to one half of the limiting value in (a)? Do not round any numbers for this part. You work should be all symbolic.) Problem #6(a): 10000000000 Enter your answer symbolically,...
1 8t(2t - 1)(t + 5) Given p(t) answer the following (t + 5)(4 – t)(7t + 2) questions: Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. a) The domain of p in interval notation is: Interval Notation: b) The t-intercept(s) are: c) The vertical asymptotes of p are at t = Write the answer(s) as just numbers separated by commas. d) p has a hole at the ordered pair: Write each...
For a certain product, cost C and revenue R are given as follows, where x is the number of units sold in hundreds. Cost: C2 = x2 + 102 VX +55 Revenue: 892(x - 5)2 + 25R2 = 16,900 dC a. Find the marginal cost dy at x = 5. The marginal cost is estimated to be $ (Do not round until the final answer. Then round to the nearest hundredth as needed.)
Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300. The balance is $ (Do not round until the final answer. Then round to the nearest cent as needed.) Enter your answer in the answer box and then click Check Answer. Clear All All parts showing O Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300. The balance is $1! (Do not round...
21² + 6 Ay The population, P, in thousands of a resort community is given 100 600t by P(t) = t20, where t is time, in months. 80-A a) Find the population at t= 0, 1, 3, and 8 months. .60 b) Find the horizontal asymptote of the graph and determine the 401 value that P(t) approaches as t goes to co? c) Explain the meaning of the answer to part (b) in terms of the 20- application 0 10...
AY 150- A company's total cost, in millions of dollars, is given by C(t) = 90 - 40e - where t is the time in years since the start-up date. The graph of C(t) is shown to the right. Find each of the following. a) The marginal cost, C'(t) b) C'(0) c) C'(5) d) Find lim C(t) and lim C'(t). t00 100 75- 0- 0 15 30 a) C'(t)=(Do not include the $ symbol in your answer.) b) C'(O) =...
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