Justin has $200 in a bank account that earns 3% in annual interest. Does this describe a linear or exponential function? Select the equation.
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Justin has $200 in a bank account that earns 3% in annual interest.
This can be modeled using an exponential function given by
[tex]f(x)=P(1+r)^x[/tex]Where P is the invested amount, r is the interest rate in decimal, and x is the number of years.
For the given case,
P = $200
r = 3% = 0.03
So, the exponential function becomes
[tex]\begin{gathered} f(x)=200(1+0.03)^x \\ f(x)=200(1.03)^x \end{gathered}[/tex]Therefore, the given situation describes an exponential function.
[tex]Exponential\colon f(x)=200(1.03)^x[/tex]