Question

Show which answer is for which, for the population question

Pool of HW problems Linear Functions Set up linear equation to solve problem (I) (1-2) DRAFT e ollowing exercises, consider this scenario: The weight of a newborm is 7.5 pounds. 1 a month for its first year. a. Find the linear function that models the baby's weight b. Find a reasonable domain and range for the function c. If the function W is graphed, find and interpret the x- and y-intercepts. d. -If the function W is graphed, find and interpret the slope of the function. e. When did the baby weight 10.4 pounds? f. What is the output when the input is 6.2? Interpret your answer. a function of the age of the baby in monthsu 1 ek For the following exercises, consider this scenario: A town has an initial population of 7 2,500 per year for 5 years 5,000. It grows at a constant rate of a. Find the linear function that models the town's population P as a function of the year, where t is the b. c. d. e. number of years since the model began. Find a reasonable domain and range for the function P If the function P is graphed, find and interpret the x-and y-intercepts. If the function P is graphed, find and interpret the slope of the function. When will the output reached 100,000? What is the output in the year 12 years from the onset of the model? In 2004, a school population was 1,001. By 2008 the population had grown to 1,697. Assume the population is changing linearly a. How much did the population grow between the year2 How long did it take the population from 004 and 2008? n to grow from 1,001 students to 1,697 students? noe napulation growth per year? 00009 Ger 2000

Answer 1

a) The linear function is : P = 75000+2500t

b) Domain : [0,5]

Range : [75000,87500]

c) If the function P is graphed , then x-intercept implies that before 30 years since the model begun, the population of the town was 0 aand y-intercept implies that when the model begun then the population of the town was 75000.

d) If the function P is graphed, then the slope of the function interprets that the population of the town increases 2500 every year.

e) Though the model is for 5 years, we assume that it also continuous after 5 years.

Then, 75000+2500t = 100000

i.e., 2500t = 25000

i.e., t = 25000/2500

i.e., t = 10

Therefore, after 10 years, the output reached 100,000.

f) When t = 12, then P = 75000+2500*12

i.e., P = 75000+30000

i.e., P = 105000

Therefore, after 12 years, the output will reach 105,000.