Interpreting Exponential Functions

What is the initial value of f(x)= a⋅b^x

• x

• b

• a

• f(x)

What is the y-intercept on f(x)=a⋅b^x ?

• x

• a

• b

• f(x)

Classify the model as Exponential GROWTH or DECAY.

f(x) = 10(1.01)^x

• Growth

• Decay

Classify the model as Exponential GROWTH or DECAY.

f(x) = 1200(.85)^x

• Growth

• Decay

A bank account earning annual compound interest was opened, and no additional withdraws or deposits were made after the initial deposit. The balance in the account after x years can be modeled by b(x)=850(1.025)^x.

Which statement is the best interpretation of one of the values in this function?

• The initial balance in the account decreases at a rate of 97.5% each year.

• The balance in the account increases at a rate of 2.5% each year.

• The initial balance of the account was $1,025.

• The balance in the account at the end of one year is $850.

Scientist are studying a bacteria sample. The function f(x)=245(1.12)^x gives the number of bacteria in the sample at the end of x days. Which statement is the best interpretation of one of the values in this function?

• The initial number of bacteria is 12.

• The initial number of bacteria decreases at a rate of 88% each day.

• The number of bacteria increases at a rate of 12% each day.

• The number of bacteria at the end of day one is 245.

The student used f(x)=5.00(1.012)^x to show how the balance in a savings account will increase over time. What does the 5.00 represent?

• The interest in the savings account earned in the first year.

• The annual interest rate of the savings account.

• The number of years the savings account has earned interest.

• The starting balance of the savings account.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x
• y = 15(1.35)^x
• y = 15(0.35)^x
• y = 35(1.15)^x

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x
• y=15,000(1.08)^x
• y=15,000(0.92)^x
• y=15,000(0.08)^x