Question

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth function represents
the number of deer y in that forest after x months? Round to the nearest thousandth.

Answer 1

Answer:

The expression that represents the number of deer in the forest is

y(x) = 50*(1.013)^x

Step-by-step explanation:

Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:

y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625

y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258

y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898

This keeps going as the time goes on, so we can model this growth with the equation:

y(x) = 50*(1 - 0.15/12)^(x)

y(x) = 50*(1.013)^x