Exponential Functions Unit

Using the equation $$y=3\left(2\right)^x$$ , answer the questions that follow.

a. Would the graph represent exponential growth or decay?

b. What is the growth or decay factor?

c. What is the percent of change?

d. What is the y-intercept of the graph?

Using the equation $$y=4\left(.7\right)^x$$ , answer the questions that follow.


a. Would the graph represent exponential growth or decay?

b. What is the growth or decay factor?

c. What is the percent of change?

d. What is the y-intercept of the graph?

Consider the two points (0, 8) and (1, 2).

a. Write a linear equation that passes through these points in slope-intercept form.

b. Write an exponential equation in y = ab^x form that also passes through the two points.

In 2000, there were 20 rabbits in Mendon Ponds Park. The population increased by 12% each year.

a. Write an equation to represent this situation where x is the time in years since 2000 and y is the rabbit population.

b. How many rabbits were there in Mendon Ponds Park in 2010?

The current student population of the Brentwood Student Center is 2,000. The enrollment at the center increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years?

Julia bought an antique dresser for $500. If the value of her dresser increases 6% annually, what will be the value of Julia's dresser at the end of 3 years to the nearest dollar?

The New York Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated. Which equation represents the number of teams, t, that remained in the tournament after r rounds.

Is the equation A = 21,000(1 - 0.12)^t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?

Sina's Print Shop purchased a new printer for $35,000. Each year, it depreciates (loses value) at a rate of 5%. What will its approximate value be at the end of the 4th year?

Mrs. Hayward invested $2,500 in a savings account for Adalyn that earns 3% interest compounded annually. If she didn't make any additional deposits or withdrawals, how much would her investment be worth in 18 years?