Question

Of all eligible voters in your county 70%, percent are currently registered to vote. A recent poll predicts that the relationship between V, the percentage of all eligible voters who are registered to vote, and t, the number of years from now will be modeled the following equation:

V=100-30*e^-0.04t
In how many years will 80% of all eligible voters in your country be registered to vote?
Give an exact answer expressed as a natural logarithm

Answer 1

-25\cdot \ln \left(\frac{2}{3}\right)

Explanation:

Answer 2

`t=-25In({(2)/(3)})\ years`

Explanation:

-Given that the percentage of voters is modeled by the function:

`V=100-30e^(-0.04t)`

We substitute for V in the function to solve for t:

`V=100-30e^(-0.04t)\\\\80=100-30e^(-0.04t)\\\\30e^(-0.04t)=20\\\\e^(-0.04t)=(2)/(3)\\\\-0.04t=In{(2)/(3)}\\\\t=In{(2)/(3)}/(-0.04)\\\\=-25In{(2)/(3)}\ years`

Hence, the number of years to hit 80% is
`-25In({(2)/(3)})\ years`