Question

A sea turtle population pis modeled by the equation p = 400 • (5/4)^y where y is the number of years since the population was first measured.
a. How many turtles are in the population when it is first measured? Where do you
see this in the equation?
b. Is the population increasing or decreasing? How can you tell from the equation?
C. When will the turtle population reach 700? Explain how you know.

Answer 1

It would take 29.3 years for the turtle population to be 700.

Exponential function

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value of y and b is the multiplier.

p represent the turtle population after y years.

Given that: $p=400(\frac{5}{4} )^y$

1. From the equation, a = 400, hence the turtle population was 400 at first.
2. b = 5/4 > 1, hence the population is increasing

For p = 700:

700 = $\frac{5}{4}^y$

log(700) = ylog(5/4)

y = 29.3 years

It would take 29.3 years for the turtle population to be 700.

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