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Maya would like to invest her money in a savings account. The function A(t)=500(1.015)t represents the amount of money Maya will have in her savings account after t years. How long will it take Maya to have $800 in her account? Round your answer to the nearest tenth of a year.

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the answer is 6 years i know this because i made this problem

Maya will have $800 in her saving account after 31.6 years.

Function representing the amount of money in Maya's saving account,

[tex]A(t)=500(1.015)^t[/tex]

Here, [tex]A(t)[/tex] = the final amount

[tex]500=[/tex] Initial amount

[tex]t=[/tex] Duration of investment

If the final amount in her saving account is $800,

Substitute the final amount as $800.

[tex]800=500(1.015)^t[/tex]

[tex](1.015)^t=\frac{800}{500}[/tex]

[tex](1.015)^t=1.6[/tex]

[tex]\text{log}(1.015)^t=\text{log}(1.6)[/tex]

[tex]t[\text{log}(1.015)]=\text{log}(1.6)[/tex]

[tex]t=\frac{\text{log}(1.6)}{\text{log}(1.015)}[/tex]

[tex]t=31.57[/tex]

[tex]t\approx31.6[/tex] years

        Therefore, Maya will have $800 in her saving account after 31.6 years.

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