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Answer 1

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.