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Halle deposited $4000 into an account that earns 5% interest each year. the growth of her investment can be expressed by the exponential equation a = 4000(1 + 0.05)t , where a is the amount in the account after t years. in how many years will her account exceed $10,000?

Respuesta :

After 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest, each year.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have an exponential equation:

[tex]\rm a = 4000(1+ 0.05)^t[/tex]

Plug a = $10,000

[tex]\rm 10000 = 4000(1+ 0.05)^t[/tex]

After calculating:

[tex]\rm 1.05^t= 2.5[/tex]

t = 18.78 ≈ 18.8 years

Thus, after 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest each year.

Learn more about the exponential function here:

brainly.com/question/11487261

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