4.3B Exponential Growth Equations

Rule of 72

• A quick and easy way to see how long it will take to double your money

• Only works for annually compounded accounts, meaning the interest rate is compounded once a year

• All you need is:

• Your interest rate

• Your initial investment

Multiple Choice

Your returns (or interest rate) are 6% a year. How long before your investment doubles?

• 18 years
• 16 years
• 12 years
• 8 years

Multiple Choice

Using the rule of 72 how many years will it take to turn $300 into $600 at an interest rate of 8%?

• 4 years

• 8 years

• 9 years

• 12 years

Multiple Choice

We have an initial investment of $1,000 we will invest at 8%.

How many years will it take to double?

$$f\left(x\right)=1,000\left(2\right)^{\frac{x}{9}}$$

• 1

• 9

• 18

• 27

Multiple Choice

We have an initial investment of $1,000 we will invest at 8%.

How many years will it take to quadruple (double twice)?

$$f\left(x\right)=1,000\left(2\right)^{\frac{x}{9}}$$

• 1

• 9

• 18

• 27

Multiple Choice

We have an initial investment of $1,000 we will invest at 8%.

How many years will it take to octuple (double three times)?

$$f\left(x\right)=1,000\left(2\right)^{\frac{x}{9}}$$

• 1

• 9

• 18

• 27

If b is...

• Greater than 1 (b>1), the function is exponential GROWTH

• Less than 1 and greater than 0 (0<b<1) the function is exponential DECAY

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​Growth vs Decay

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Multiple Choice

Is $$f\left(x\right)=100\left(.2\right)^x$$ growth or decay?

• Growth
• Decay
• Beans

Multiple Choice

Which of the following is an example of exponential growth?

• y = 80(.5)^x

• y = .2(.8)^x

• y = .2(6)^x

• y = 50(.9)^x

Multiple Choice

$$f\left(x\right)=100\left(.2\right)^x$$

This equation represents _% being (added/subtracted) from the total every t years.

• 20% added

• 20% subtracted

• 80% added

• 80% subtracted

Multiple Choice

$$f\left(x\right)=100\left(1.4\right)^x$$

This equation represents _% being (added/subtracted) from the total every t years.

• 40% added

• 40% subtracted

• 60% added

• 60% subtracted

Multiple Choice

$$f\left(x\right)=100\left(.85\right)^x$$

This equation represents _% being (added/subtracted) from the total every t years.

• 15% added

• 15% subtracted

• 85% added

• 85% subtracted