Question

find the derivative of the following function.
a = 700(1.661)^t
a =
(type an exact answer.)

Explanation:

Step1: Recall the derivative formula for \(y = a\cdot b^x\)

The derivative formula for \(y=a\cdot b^{x}\) is \(y^\prime=a\cdot b^{x}\cdot\ln(b)\). In the given function \(A = 700(1.661)^{t}\), we have \(a = 700\) and \(b=1.661\).

Step2: Apply the formula

Using the formula \(A^\prime=a\cdot b^{t}\cdot\ln(b)\), substitute \(a = 700\) and \(b = 1.661\) into it. So \(A^\prime=700\times(1.661)^{t}\times\ln(1.661)\)

Answer:

\(700\times(1.661)^{t}\times\ln(1.661)\)