Solve the equation.

Question

An endangered species of bird has a population that is modeled by the exponential equation

A = 1500e^kt, where A (in hundreds) represents the current population of the birds t years
from now.         

a. Scientists recently discovered the k-value, or rate of the bird population change, to be ^-0.23

Write a function that gives the current population.      

b. Tell whether your function in part (a) represents exponential growth or exponential decay.

c. What will the population be 6 years from now?

 

 

 

 

 

Answer 1

A=1500eᵏᵗ.

(a) If k=-0.23, then function A(t)=1500e⁻⁰˙²³ᵗ, where A is the population in hundreds.

(b) Exponential decay.

(c) When t=6, A(6)=1500e⁻¹˙³⁸=377.37.

This means that the population will decline to 37,737 according to the model.