Question

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

Explain why the money in Nico's saving account over time is an example of exponential growth

Nico's savings account is an example of exponential growth because it is _________ each year by a factor of ____
(First dropdown answers: increasing, decreasing. Second dropdown answers: 1.08, 0.08, 1.8, 8, 0.8)

Create a sequence that describes the amount of money in Nico's saving account each year for 8 years (Write answers in this format: 2,000 or 1,456.78)
$__, $__, $__, $__, $__, $__, $__, $__


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
y = __(__)^x

Use your formula to find the amount of money in Nico's savings account after 18 years.

After 18 years, Nico has $__ in his savings account

Answer 1

Explain why exponential: The account increases by the same percent (8%) each year, so each year the amount is multiplied by the same factor → exponential growth.

Fill-in: increasing each year by a factor of 1.08

Sequence for 8 years (starting at birth): $1,000, $1,080, $1,166.40, $1,259.71, $1,360.49, $1,469.33, $1,586.87, $1,713.82

Formula: y = 1000(1.08)^x where x = years since Nico was born.

After 18 years: y = 1000(1.08)^18 ≈ $3,996.02