we are supposed to find
The derivative of the function [tex] A=620(1.786)^t [/tex]
Differentiate both the sides wit respect to t we get
[tex] \frac{dA}{dt}=\frac{d620(1.786)^t }{dt}\\
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\text{Take out the constant term we get}\\
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\frac{dA}{dt}=620\frac{d(1.786)^t }{dt}\\
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\text{Now using the formula }\\
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\frac{da^x}{dx}=(lna) a^x\\
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\frac{dA}{dt}=620*ln(1.786)(1.786)^t\\
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\frac{dA}{dt}=359.587(1.786)^t\\ [/tex]
