You might need: Calculator Yasemin deposited $1000 into a savings account. The relationship between the time, t, in years,

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Yasemin deposited $1000 into a savings account.
The relationship between the time, t, in years, since the account was first opened, and Yasemin’s account
balance, B(t), in dollars, is modeled by the following function.
B(t) = 1000. 20.03
How many years will it take for Yasemin’s account balance to reach $1500?
Round your answer, if necessary, to the nearest hundredth.

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Gianna 2 months 2021-10-15T14:01:56+00:00 1 Answer 0 views 0

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    2021-10-15T14:03:43+00:00

    Answer:

    The number of years it will take for Yasemin’s account balance to reach $1500 is 13.52 years.

    Step-by-step explanation:

    Where the model of the relationship between the time, t, in years, since the account was first opened and the and the balance in Yasemin’s account is presented as follows;

    B(t) = 1000 \times e^{(0.03 \times t)}

    To find find out how many years it will take for Yasemin’s account balance to reach $1500, we substitute B(t) = $1500 since we are told that after the years his account balance became $1500 as follows;

    \$ 1500 = 1000 \times e^{(0.03 \times t)}

    We now solve for t

    \$ 1500 = 1000 \times e^{(0.03 \times t)}\\\\\frac{1500 }{1000 } =  e^{(0.03 \times t)}\\1.5 = e^{(0.03 \times t)}\\\\ln(1.5) = ln (e^{(0.03 \times t)})\\\\ln(1.5) = (0.03 \times t) \times ln (e)\\\\\therefore ln(1.5) = (0.03 \times t) \\\\t = \frac{ln(1.5)}{0.03 }  = 13.52 \ years

    The number of years it will take for Yasemin’s account balance to reach $1500 = 13.52 years.

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