Question

Please help me!!!!!!!!!!

Answer 1

3.0 years

Explanation:

The value of a certain account (in dollars) after t years is given by the equation:

`B = 300 * 1.3^t`

To determine how long it will take for the value of the account to increase to $660, substitute B = 660 into the given equation and solve for t:

`300 * 1.3^t=660`

Divide both sides of the equation by 300:

`(300 * 1.3^t)/(300)=(660)/(300)`

`1.3^t=2.2`

Take natural logs of both sides of the equation:

`\ln(1.3^t)=\ln(2.2)`

Apply the log power rule:

`t\ln(1.3)=\ln(2.2)`

Divide both sides of the equation by ln(1.3):

`(t\ln(1.3))/(\ln(1.3))=(\ln(2.2))/(\ln(1.3))`

`t=(\ln(2.2))/(\ln(1.3))`

`t=3.0052010397...`

`t=3.0\; \sf (1\;d.p.)`

Therefore, it will take 3.0 years for the account value to increase to $660.