Suppose b(t) is the length of a bamboo shoot, measured in millimeters, at time tt, measured in years. Then b′(t)represen...
Suppose b(t) is the length of a bamboo shoot, measured in millimeters, at time tt, measured in years. Then b′(t)represents the rate at which the length is changing at time tt, and b′′(t) is the rate at which the rate of change is changing at time tt.
The units for b′′(t)are
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Suppose b(t) is the length of a bamboo shoot, measured in millimeters, at time tt, measured in years. Then b′(t)represen...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 1...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 10. (Suggestion: First solve the differential equation using anti-differentiation.) Does the answer to this question depend on the initial condition L(0)? (b) Determine L(t) if L(0)=2 2. Continued (c) Find the approximate change in length of...
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years. Find the rate at which the balance is changing when t = 1 year, t = 10 years, and 50 years. (Ro...
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years. Find the rate at which the balance is changing when t = 1 year, t = 10 years, and 50 years. (Round your answers to two decimal places.) (a) t-1 year per year (b) t10 years per year (c)50 years per year
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years....
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of cha...
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of change of P is given by 7600e0.4t fish/year. dt(19 + e0.4t)2 dp dt a. Graph on the domain [0, 20]. Make sure your graph is properly labeled. b. Estimate the change in population on the time interval 0 s t š 20 years. Use 10 intervals, each lasting two years. Use rate of change data from the left side of...
(18 marks) Suppose that the Phillips curve is given by: TT. = + 0.2 – 5ugs...
(18 marks) Suppose that the Phillips curve is given by: TT. = + 0.2 – 5ugs with people’s expectation of inflation governed by: T = 11-14 At time t = 0, it is known that the economy is in a medium run equilibrium with inflation rate of 3%. a. Find the natural rate of unemployment for this economy. (3 marks) b. If starting t = 1, the government decided to keep unemployment rate permanently at 3%. Find the expected inflation...
6. The size b of a bacteria population at time t (measured in hours) is given...
6. The size b of a bacteria population at time t (measured in hours) is given by b(t) = 106 + 10't - 10342. Calculate the relative growth rate when t = 5. Answer for Question 6.
Suppose the length of time Y (in years) that a malaria patient spends in remission has...
Suppose the length of time Y (in years) that a malaria patient spends in remission has pdf 9 What is the average length of time that a patient spends in remission?
of the particle at any time t (where t is measured in seconds) (b) Find the...
of the particle at any time t (where t is measured in seconds) (b) Find the MacBook Air
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies t...
help with part b
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies the differential equation y' 0.05y - 10,000. (a)Suppose that after one year the balance is $180,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y k(y M) (c)Describe the differential equation in words. (a) The balance is...
3. The wave heights h in the open sea depend on the speed v of the wind and the length of time t ...
3. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h(v, t) have been experimentally determined and the results are recorded in feet in the following table. Here wind speed v is measured in knots and the duration t is measured in hours h(t, v)t 5 t-10 t 15 t 20 t 30 t-40...
(1 point) Suppose that t years from now, one investment plan will be generating profit at the rat...
(1 point) Suppose that t years from now, one investment plan will be generating profit at the rate of P (1) = 90 + 12 hundred dollars per year, while a second investment will be generating P(I) = 258 + 21 hundred dollars per year. a. For how many years does the rate of profitability of the second investment exceed that of the first? Answer: b. Compute the net excess profit, in hundreds of dollars, assuming that you invest in...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 10. (Suggestion: First solve the differential equation using anti-differentiation.) Does the answer to this question depend on the initial condition L(0)? (b) Determine L(t) if L(0)=2 2. Continued (c) Find the approximate change in length of...
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years. Find the rate at which the balance is changing when t = 1 year, t = 10 years, and 50 years. (Round your answers to two decimal places.) (a) t-1 year per year (b) t10 years per year (c)50 years per year
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years....
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of change of P is given by 7600e0.4t fish/year. dt(19 + e0.4t)2 dp dt a. Graph on the domain [0, 20]. Make sure your graph is properly labeled. b. Estimate the change in population on the time interval 0 s t š 20 years. Use 10 intervals, each lasting two years. Use rate of change data from the left side of...
(18 marks) Suppose that the Phillips curve is given by: TT. = + 0.2 – 5ugs with people’s expectation of inflation governed by: T = 11-14 At time t = 0, it is known that the economy is in a medium run equilibrium with inflation rate of 3%. a. Find the natural rate of unemployment for this economy. (3 marks) b. If starting t = 1, the government decided to keep unemployment rate permanently at 3%. Find the expected inflation...
6. The size b of a bacteria population at time t (measured in hours) is given by b(t) = 106 + 10't - 10342. Calculate the relative growth rate when t = 5. Answer for Question 6.
Suppose the length of time Y (in years) that a malaria patient spends in remission has pdf 9 What is the average length of time that a patient spends in remission?
of the particle at any time t (where t is measured in seconds) (b) Find the MacBook Air
help with part b
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies the differential equation y' 0.05y - 10,000. (a)Suppose that after one year the balance is $180,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y k(y M) (c)Describe the differential equation in words. (a) The balance is...
3. The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h(v, t) have been experimentally determined and the results are recorded in feet in the following table. Here wind speed v is measured in knots and the duration t is measured in hours h(t, v)t 5 t-10 t 15 t 20 t 30 t-40...
(1 point) Suppose that t years from now, one investment plan will be generating profit at the rate of P (1) = 90 + 12 hundred dollars per year, while a second investment will be generating P(I) = 258 + 21 hundred dollars per year. a. For how many years does the rate of profitability of the second investment exceed that of the first? Answer: b. Compute the net excess profit, in hundreds of dollars, assuming that you invest in...
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