Try It 10.87: Evaluating an Exponential Growth Model

As a data analyst forecasting the exponential growth of your company's new software platform, you need to project the future number of active users. Recall the standard procedure for solving an exponential growth application and arrange the following mathematical steps in the correct order.

A logistics company is monitoring the growth of its delivery fleet. The number of vehicles is growing exponentially following the formula $A = A_0 e^{kt}$, where $A$ is the final amount, $A_0$ is the initial amount, $k$ is the growth rate, and $t$ is the time in years. If the company started with 50 vehicles and now has 150 vehicles after 3 years, which equation is correctly set up to solve for the growth rate $k$?

As a cloud infrastructure analyst, you use the exponential growth formula $A = A_{0} e^{kt}$ to project future data storage requirements for your organization. Match each mathematical component of the formula with its corresponding role in this capacity planning scenario.

In a professional growth analysis using the exponential model $A = A_0 e^{kt}$, if the growth rate constant $k$ is unknown, it is necessary to first calculate the value of $k$ using current data before you can determine the projected future amount $A$.

Procedural Steps in Exponential Growth Forecasting

A digital marketing analyst is tracking the growth of a company's email subscriber list using the exponential growth model $A = A_0 e^{kt}$. If the list grows from an initial size of 100 subscribers to 300 subscribers in 3 weeks, substituting these values yields the equation ${}300 = 100 e^{3k}$. After dividing both sides by 100 to get ${}3 = e^{3k}$, the analyst must take the ____ logarithm of both sides of the equation to solve for the weekly growth rate $k$.

Projecting Fulfillment Center Volume