Question

Find the logarithmic derivative
A(t)=500e^0.07t

Answer 1

$A(t)=500e^{0.07t}\\ \\ \frac{dA(t)}{dt} = \frac{d}{dt}(500e^{0.07t}) \\ \\ \Rightarrow \frac{dA(t)}{dt} = 500 \times \frac{d}{dt}(e^{0.07t}) \\ \\ \Rightarrow \frac{dA(t)}{dt} = 500 \times e^{0.07t} \times \frac{d}{dt}(0.07t) \\ \\ \Rightarrow \frac{dA(t)}{dt} = 500 \times e^{0.07t} \times 0.07 \\ \\ \Rightarrow \frac{dA(t)}{dt} =35e^{0.07t}$