Exponential Functions

Open Ended

Why do you think exponential functions are important in real-life situations?

Multiple Choice

Which of the following is an example of reasoning abstractly and quantitatively in mathematics?

• Solving a word problem by translating it into an equation

• Memorizing multiplication tables

• Copying answers from a textbook

• Ignoring units in calculations

Multiple Choice

How does the behavior of the exponential function change as x increases or decreases?

• It increases rapidly as x increases and decreases slowly as x decreases.

• It decreases rapidly as x increases and increases slowly as x decreases.

• It remains constant regardless of x.

• It oscillates as x increases or decreases.

Open Ended

Explain why the graph of an exponential function passes through the points (0, 1) and (1, a).

Fill in the Blanks

Exponential growth or decay occurs when the amount a quantity increases by is proportional to its size.

Write the correct answer in the blank.

Multiple Select

Which of the following are examples of quantities that grow exponentially?

• Investments with a fixed compound interest rate

• The number of microorganisms in a culture dish

• Population size

• The rate at which an object cools

Multiple Choice

Which of the following statements about exponential decay is correct?

• The smaller the quantity becomes, the more slowly it decays.

• The smaller the quantity becomes, the faster it decays.

• The rate of decay is constant regardless of size.

• Exponential decay only applies to radioactive materials.

Open Ended

What are some real-world examples of exponential decay?

Multiple Choice

What is the function that models the growth of a population of 100 bacteria that doubles every minute?

• N = 100 × 2^t

• N = 100 × t^2

• N = 2 × 100^t

• N = 100 × t

Open Ended

Where will Hayden have the highest salary after 3 years? Where will Hayden have the highest salary after 5 years?

Multiple Choice

If you invest $1000 at a 7% annual interest rate for 3 years, how much money will you have when the account matures if interest is compounded monthly?

• $1225.04

• $1210.00

• $1230.00

• $1200.00

Multiple Choice

What claim is being tested about compounding interest in the scenario described?

• That compounding more frequently can make the amount as large as desired

• That compounding less frequently gives more money

• That the interest rate does not matter

• That the principal amount does not affect the outcome

Fill in the Blanks

Fill in the blank: The number denoted by

is an irrational number approximately equal to 2.718.

Multiple Choice

Which of the following describes the graph of f(x) = e^x?

• It increases rapidly for positive x and approaches zero for negative x.

• It decreases rapidly for positive x and increases for negative x.

• It is a straight line passing through the origin.

• It is a parabola opening upwards.

Open Ended

Explain how the parameters y₀ and k affect the shape and position of exponential growth and decay functions.

Multiple Choice

Which of the following best describes the difference between an exponential growth function and an exponential decay function?

• Exponential growth increases over time, while exponential decay decreases over time.

• Exponential growth decreases over time, while exponential decay increases over time.

• Both exponential growth and decay increase over time.

• Both exponential growth and decay decrease over time.

Multiple Choice

The formula m = 15e^{-0.083t} models the decay of a radioactive iodine sample. What is the value of m when t = 0?

• 15

• 0

• -0.083

• 1

Fill in the Blanks

The mass of the sample after 2 days is

g.

Fill in the Blanks

The mathematical skill that involves making sense of problems and persevering in solving them is called

.

Open Ended

Which mathematical skill do you think is most important when learning about exponential functions, and why?