Using an exponential function, it is found that it would take 9 years for the prices to double.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
Inflation of 8% means that r = 0.08. The time to double is t for which A(t) = 2A(0), hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]2A(0) = A(0)(1.08)^t[/tex]
[tex](1.08)^t = 2[/tex]
[tex]\log{(1.08)^t} = \log{2}[/tex]
[tex]t\log{1.08} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.08}}[/tex]
[tex]t = 9[/tex]
It would take 9 years for the prices to double.
More can be learned about exponential functions at https://brainly.com/question/25537936
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