Question

Create a question with this scenario you could ask that could be answered only by graphing or using logarithm.

David estimated he had about 20 fish in his pond. A year later, there were about 1.5 times as many fish. The year after that, the number of fish increased by a factor of 1.5 again. The number of fish is modeled by f(x)=20(1.5)^x.

Answer 1

After how many years is the fish population 100?

x=3.97 years

Explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

`f (x) = 20 (1.5) ^ x`

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 100?

So we do
`f (x) = 100` and solve for the variable x

`100 = 20 (1.5) ^ x\\\\(100)/(20) = (1.5)^x\\\\ 5= (1.5)^x\\\\log_(1.5)(5) = log_(1.5)(1.5)^x\\\\log_(1.5)(5) = x\\\\x =log_(1.5)(5)\\\\x=3.97\ years`

Observe the solution in the attached graph