Using Exponential Functions

Question

The population of golden finches is deceasing at a rate of 3.5% every 2 years. You have counted 80 of the animals in the habitat you are studying. To the nearest whole number, how many golden finches will be left in the habitat in 15 years?

Answer 1

Hi! In order to solve this, you will need the exponential decay function: y = a(1 - b)^x. 'y' represents the number of finches that will remain after 15 years, 'a' is the original number of finches, 'x' is the amount of time passed, and 'b' is the rate at which the population of finches is decreasing.

We must keep in mind, however, that it says 3.5% per 2 years. So to get the rate of decrease per year, we must divide 3.5% by 2. After doing so, we get 1.75%. Then, we must convert this percentage into a decimal, so that would be 0.0175.

Now, to do some plugging and chugging:

y = 80(1 - 0.0175)^15

y = 61.39 finches

But since the instructions ask that we round to the nearest whole number, there will be 61 finches remaining after 15 years.

Answer: 61 finches

Answer 2

This is an example of exponential decay. The exponential decay law for this problem is

p(t) = 80 (1 - 0.035)^t/2

p(t) = 80 (0.965)^t/2

where t is years elapsed from when the population was 80. Plug in t=15 and evaluate.