How do you find out how much time it will take the money in your

bank account to double?

For example:If you have $100 in the bank, how long until you earn $100 interest?

In this lesson you will learn how to create and solve exponential equations

by using a table of values

Let’s Review

40% growth 40% growth

Example: You start with 25 dots, and the number of dots increase by 40% in every step.

Let’s Review

y = a(1+r)x

y = 25(1+.4)x

y = 25(1.4)x

40% growth 40% growth

A Common Mistake

Growth Factor > 1 (example 1.4)

0 < Decay Factor < 1 (example 0.4)

Core Lesson

Years Balance

0 400

1 424

2 449.44

3 476.41

4 504.99

Your bank account has grown according to the data shown in the table. Write an equation and find out how long your account will

take to reach a balance of $600?

Core Lesson y = a(1+r)x

y = (400)*(1+r)xy = (400)*1.06x

VERIFY: what does my answer mean? does this make sense?

x ≈ 7 years

600 = (400)*1.06x

Years Balance

0 400

1 424

2 449.44

3 476.41

4 504.99

In this lesson you have learned how to create and solve exponential equations

by using a table of values

Guided Practice

Years Value

0 25000

1 21250

2 18063

When you buy a new car, its value quickly “depreciates”, or, loses

value according to the data seen here. Approximately how long will it take for your car’s value to fall

to $13000?

Guided Practice y = a(1+r)x

y = (25000)*(1+r)xy = (25000)*.85x

VERIFY: what does my answer mean? does this make sense?

x ≈ 4 years

13000 = (25000)*.85x

Years Value

0 25000

1 21250

2 18063

Extension Activities

a. Investigate the interest rates of a few different bank accounts and evaluate which is a better account for your money. Don’t forget to look for monthly vs. annually compounding interests!

b. Explore the math function called “logarithm”, and investigate how the “logarithm” can help you solve exponentials.

Quick Quiz

1. Your bank account is compounded 6% annually (every year). If you put $500 to start, in how many years will your bank account reach $1000?

2. Polar bear populations have been on the decline recently. If the population is decreasing at a rate of 13% each year, how long will it take an original population of 7000 to reach 4000?