Question

Of all eligible voters in your county, 70\%70%70, percent are currently registered to vote. A recent poll predicts that the relationship between VVV, the percentage of all eligible voters who are registered to vote, and ttt, the number of years from now will be modeled by the following equation. V=100-30\cdot e^{-0.04t}V=100−30⋅e −0.04t V, equals, 100, minus, 30, dot, e, start superscript, minus, 0, point, 04, t, end superscript In how many years will 80\%80%80, percent of all eligible voters in your county be registered to vote? math

Answer 1

-25 x Ln(2/3) years

Explanation:

Answer 2

10.14 years

Explanation:

The following equation describes the percentage of all eligible voters that are registered to vote as a function of time:

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

The time 't' for which V(t) = 80 is the amount of years required for the percentage of registered voters to reach 80%:

`80=100-30e^(-0.04t)\\(20)/(30)= e^(-0.04t)\\ln((2)/(3))=-0.04t*ln(e)\\ t=10.14\ years`

It will take 10.14 years until 80% of all eligible voters in your county are registered to vote