The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 25500. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer)

The number of acres of old growth forest in a park, N, initially 500 acres, is decreasing at a continuous rate of 15% per year. A possible formula for N as a function of t, measured in years, is: O (a) N-500 (1.15) O (b) N = 500 (0.85) O (c) N =500 (0.15) O (d) N-500 (-0.15) O (e) N= 500e1.15t O (f) N = 500e0.85t O(g) N-500e0.15t O (h) N-500e-0.15t O (i) N-500 - 15t O (₁) N-500-0.15t

On a cool autumn evening of 70 degrees Fahrenheit, Detective Albert Gebra is investigating a murder/crime scene. Al assumes that the victim had a normal body temperature of 98.6 degrees Fahrenheit when he died (at time m =0) and Al finds that the body cooled from 85.7 degrees to 81.3 degrees in 11 minutes. (a) Use this information to find the constants in the function and clearly state your complete model. You may use the nspire to solve any algebraic equation as long as the equation that you are solving is clearly identified. 2. (b). If at 9:48 PM the body temperature was taken to be 78.4 degrees, use your model to estimate the time of death. Show all steps.

2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.

This exercise uses the population growth model. A culture starts with 9000 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.) n(t) =     (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) bacteria (c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) hr

Example 62(b). A firm produces 36,000 items per year. It costs Rs. 250 to make the machine run regardless of the number (x) of items produced in a run. The cost of storage is 50 paise per item per year on average inventory x/2 in hand. The cost of material per item is Rs. 5. Find the economic lot size x.

A population numbers 17,000 organisms initially and grows by 5.3% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = abt, where P =