Question

kathleen is a biologist studying the frogs at pinecrest lake. she is concerned about their decline, so she keeps track of their numbers. this table shows the frog population each year since kathleen started recording data. frog population years since initial recording (x) 0 1 2 3 4 5 population (y) 197 179 159 145 132 116 here is the exponential function that best fits the data. y = 198(0.9)^x use the exponential function to complete the sentence below. according to the function, the frog population at pinecrest lake will be 100 between years after the initial recording.

Explanation:

Step1: Set y = 100 in the function

$100=198(0.9)^{x}$

Step2: Solve for x

First, divide both sides by 198: $\frac{100}{198}=(0.9)^{x}$, so $0.50505=(0.9)^{x}$.
Then, take the natural - logarithm of both sides: $\ln(0.50505)=x\ln(0.9)$.
Finally, $x = \frac{\ln(0.50505)}{\ln(0.9)}\approx6.5$.

Answer:

6 and 7