Respuesta :
Using the given exponential function, it is found that it will take 1.5 years for the amount of savings to double from the initial amount deposited of $1250.
Exponential function:
The exponential function that models the savings in the bank account is given by:
[tex]S(t) = 1250e^{0.45t}[/tex]
- In which t is the time in years that the money has been in the account.
The time to double from the initial amount deposited of $1250 is t for which S(t) = 2(1250) = 2500, hence:
[tex]S(t) = 1250e^{0.45t}[/tex]
[tex]2500 = 1250e^{0.45t}[/tex]
[tex]e^{0.45t} = \frac{2500}{1250}[/tex]
[tex]e^{0.45t} = 2[/tex]
[tex]\ln{e^{0.45t}} = \ln{2}[/tex]
[tex]0.45t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.45}[/tex]
[tex]t = 1.5[/tex]
It will take 1.5 years for the amount of savings to double from the initial amount deposited of $1250.
To learn more about exponential functions, you can take a look at https://brainly.com/question/14855561
