Understanding Exponential Models

The video tutorial explores exponential models through three examples: locust population growth, bear population decline, and tree branch growth. It explains how exponential functions model these changes over time, using tables to illustrate the calculations. The locust population grows by a factor of 1.85 daily, the bear population decreases by two-thirds annually, and tree branches increase by 75% each year. The tutorial emphasizes understanding exponential growth and decay in real-world contexts.

What is the main focus of the Khan Academy exercise discussed in the video?

• Interpreting rate of change for linear models

• Interpreting rate of change for exponential models

• Understanding quadratic equations

• Solving algebraic expressions

What is the initial number of locusts at the start of the model?

• 850 locusts

• 750 locusts

• 1000 locusts

• 500 locusts

By what factor does the locust population grow each day?

• 2.0

• 1.85

• 1.5

• 1.25

What is the initial bear population in the Siberia model?

• 2000 bears

• 1800 bears

• 2187 bears

• 2500 bears

By what factor does the bear population decrease each year?

• One-third

• Two-thirds

• Half

• Three-quarters

What is the initial number of branches on Akiba's tree?

• 60 branches

• 42 branches

• 50 branches

• 30 branches

By what percentage do the branches on Akiba's tree increase each year?

• 75%

• 60%

• 50%

• 80%

If a population grows by 200%, how many times larger does it become?

• Five times larger

• Four times larger

• Three times larger

• Two times larger

What happens to a population if it grows by a factor of one?

• It doubles

• It halves

• It remains constant

• It triples

If a population grows by 10%, what is the growth factor?

• 1.3

• 1.4

• 1.2

• 1.1