Calculating Rate of Change from Exponential Functions

Which equation describes the story below?

You start with $5 and triple your money every day.

• y=5(3)^x

• y=5^x

• y=5(3x)

• y=15^x

Write an exponential function to model the situation. Then solve.

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

• C(t) = 12000(1.06)^t ; $3149.72

• C(t) = 12000(.06)^t ; $3149.72

• C(t) = 12000(.06)^t ; $1472.95

• C(t) = 12000(1.06)^t ; $15149.72

Write an exponential function to model the situation. You invest $1500. Your investment increases at a rate of 3.5%.

• B(t) = 1500(0.965)^t

• B(t) = 1500(1.035)^t

• B(t) = 1500(.035)^t

• B(t) = 1500(1.965)^t

The equation f(x) = 300(1.06)^x is being used to calculate the amount of money in a savings account.  What does the 1.06 represent?

• 6% growth

• 6% decay

• 1.06% growth

• .06% decay

• A/F
• B/G
• C/H
• D/J

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

What type of function is y = 7(5/4)^x?

• Exponential Growth

• Exponential Decay

• Linear

• None of the above

• Because the 25 was bigger than one

• Because the 0.20 was bigger than one

• Because the 25 was less than one

• Because the 0.20 was less than one