Answer :
The equation f(t) = 210(1.31)^t can be written in the form f(t) = ae^(kt), where a = 210 and k ≈ 0.265 (rounded to three decimal places).
To convert the equation f(t) = 210(1.31)^t to the form f(t) = ae^kt, we need to rewrite it in terms of the base e instead of the base 1.31.
Now, let's break down the computation into steps:
Step 1: Rewrite the equation using the natural base e
The equation f(t) = 210(1.31)^t can be rewritten using the natural base e by applying the logarithmic property:
f(t) = 210(e^(ln(1.31))^t.
Step 2: Simplify the equation
Since ln(1.31) is a constant value, we can simplify the equation further:
f(t) = 210(e^(kt)).
Here, k = ln(1.31).
Therefore, the equation f(t) = 210(1.31)^t can be written in the form f(t) = ae^(kt), where a = 210 and k ≈ 0.265 (rounded to three decimal places).
By following these steps, you can convert the given equation to the form f(t) = ae^(kt), where a and k are the corresponding values determined from the original equation.
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