Understanding Linear and Exponential Growth

This video tutorial compares linear and exponential growth models, explaining both recursive and explicit equations for each. It provides examples using elk population growth and car depreciation to illustrate the differences between linear and exponential growth. The tutorial also includes a comparison of the two models and their graphical representations, highlighting how exponential growth can lead to faster increases compared to linear growth.

What is the main difference between linear and exponential growth?

• Linear growth increases by a constant percentage, while exponential growth increases by a constant amount.

• Both linear and exponential growth increase by a constant percentage.

• Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

• Both linear and exponential growth increase by a constant amount.

In a linear growth model, if the initial quantity is P0 and it grows by D units every period, what is the explicit formula?

• P_n = P_0 * D^n

• P_n = P_0 + D * n

• P_n = P_0 * D * n

• P_n = P_0 + D^n

For exponential growth, if the initial quantity is P0 and it grows by R percent every period, what is the recursive formula?

• P_n = P_0 + R * n

• P_n = (1 + R) * P_n-1

• P_n = P_0 * (1 + R)^n

• P_n = P_n-1 + R

In the example of the elk population, what is the growth rate used in the exponential model?

• 20%

• 25%

• 15%

• 10%

When comparing linear and exponential growth, which model shows a faster increase in population over time?

• Linear growth

• Both increase at the same rate

• Exponential growth

• Neither, they both decrease

In the Flagstaff population example, what is the common difference used in the linear growth model?

• 1,500

• 1,300

• 1,200

• 1,000

What is the predicted population of Flagstaff in 5 years using the linear growth model?

• 71,500

• 73,000

• 70,000

• 72,500

In the car depreciation example, what is the multiplier used in the exponential decay model?

• 0.7

• 0.9

• 1.0

• 0.8

How much will the car be worth in 5 years according to the exponential decay model?

• $6,500

• $6,000

• $5,898.24

• $5,000

Which of the following is an example of exponential decay?

• A population increasing by 1,000 people per year

• A car losing 20% of its value each year

• A bank account earning 5% interest annually

• A tree growing 2 feet taller each year