Differentiate the exponential function

Make n the subject of the formula given that PV^n=c

how long will it take for the population of a certain country to quadruple if its annual growth rate is 2.5% round to the nearest year.

Growth model: 
 
which we simplify to get 

 
solving for t ... 
 


 
this is about 81 years

Find the range of the function f(x)= 8^x - 24 a. -infinity, -24, b. -24, infinity, c. -infinity, infinity, d. -24, 0

b) because the exponential function decays to 0 but grows indefinitely 

:)

Differentiate the exponential function

Find the derivative of  the function:

Solution:

Logarithmic differentiation is a very efficient way to evaluate this derivative:

Limit of an exponential function

Limits of exponential functions sometimes call for L'Hopital's Rule. In this example the limit is much easier to compute after we apply the rule.