Applied calculus

Question

Write the function below in the form Upper P equals Upper P Subscript 0 Baseline a Superscript t. Is this exponential growth or exponential decay?

 

P=2e^-2.3t

 

Round the base of the exponential function, a, to four decimal places.

Answer 1

This is an exponential decay problem because your exponential power is negative (-2.3t)

 

The integral of e^ax is (e^ax)/a

 

The integral of the above problem is (e^-2.3t)/-2.3 with limits of 0 and 1 for the x values.

 

(1/-2.3)*((e^-2.3(1)) - (e^-2.3(0)))

 

(1/-2.3)*(0.10026 - 1.00000)

 

0.3912