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The formula A=Pe^(0.04t) gives the amoun...

The formula `A=Pe^(0.04t)` gives the amount A that a savings account will be worth if an initial investment P is compounded at an annual rate of 4 percent for t years. Under these conditions, how many years will it take an initial investment of $10,000 to be worth approximately $25,000?

A

1.9

B

2.5

C

9.9

D

22.9

Text Solution

Verified by Experts

The correct Answer is:
D
Substitute the given values into the formula to get 25,000=`10,000e^(0.04t)`. To solve for t, first divide both sides by 10,000. then take the ln of both sides to get `ln2.5=0.04t`. Therefore `t=(ln2.5)/(0.04)=22.9`
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