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I am having trouble understanding how to change the form of an exponential function. Can someone explain the process in which the function below

$$T(t) = e^{-0.0407409t+3.89467} +26$$

is changed into this form.

$$T(t) = 49.1398 e^{-0.0407409 t} + 26$$

Thanks

DMcMor
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Unknown Person
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    This follows from the exponent rule $e^{a+b}=e^a \cdot e^b$. For this example, we have $e^{-0.0407409t+3.89467} = e^{-0.0407409t} \cdot e^{-3.89467}$. And $e^{3.89467} \approx 49.1398$. – Nicholas Roberts Nov 26 '20 at 01:39

1 Answers1

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Starting with $$T(t) = e^{-0.0407409t+3.89467} +26$$ we can use rules of exponents to rewrite the first term as $$e^{-0.0407409t}e^{3.89467},$$ and since $$e^{3.89467} \approx 49.1398$$ we can say that $$T(t) \approx 49.1398e^{-0.0407409t} +26.$$ Note that you really shouldn't say that $$T(t) = 49.1398e^{-0.0407409t}$$ because some rounding was done to go from $e^{3.89467}$ to $49.1398$.

DMcMor
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