When Nico was born, his grandparents put $1000 in a special savings account. The amount of money in the savings account increases by 8% every year. Nico tracks how much money is in the account over time.

Question

Explain why the money in Nico’s savings account over time is an example of exponential growth.
Create a sequence that describes the amount of money in Nico’s savings account each year for 8 years
Create a formula for the amount of money in Nico’s savings account over time
y = a⋅b^x
a= initial amount
b= growth factor
Use your formula to find the amount of money in Nico’s savings account after 18 years.

Answer 1

The money in Nico's savings account over time is an example of exponential growth because it increases by a consistent percentage every year. In this case, it increases by 8% each year, which means the growth rate remains constant.

To create a sequence that describes the amount of money in Nico's savings account each year for 8 years, we can start with the initial amount of $1000 and calculate the amount after each year by multiplying the previous year's amount by 1.08 (which represents a 8% increase):

Year 1: $1000 * 1.08 = $1080
Year 2: $1080 * 1.08 = $1166.40
Year 3: $1166.40 * 1.08 = $1259.71
Year 4: $1259.71 * 1.08 = $1360.48
Year 5: $1360.48 * 1.08 = $1469.33
Year 6: $1469.33 * 1.08 = $1587.52
Year 7: $1587.52 * 1.08 = $1716.12
Year 8: $1716.12 * 1.08 = $1856.96

Using the formula y = a⋅b^x, we can say that the amount of money in Nico's savings account after x years is equal to the initial amount (a) multiplied by the growth factor (b) raised to the power of x.

In this case, a = $1000 (the initial amount) and b = 1.08 (the growth factor of 8%).

So, the formula for the amount of money in Nico's savings account over time is:

y = 1000⋅1.08^x

To find the amount of money in Nico's savings account after 18 years, we can substitute x = 18 into the formula:

y = 1000⋅1.08^18
y = 1000⋅(1.08^18)
y ≈ 1000⋅2.729
y ≈ $2729

Therefore, the amount of money in Nico's savings account after 18 years is approximately $2729.