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.
A. Explain why the money in Nico's account over time is an example of exponential growth.
B. Create a sequence that describes the amount of money in Nico's savings account each year for 8 years.
A. The money in Nico's account over time is an example of exponential growth because it is increasing at a constant rate (8%) each year. This means that the amount of money in the account is not growing by a fixed dollar amount each year, but rather by a percentage of the previous balance. This exponential growth pattern is characteristic of exponential functions.
B. To create a sequence describing the amount of money in Nico's savings account each year for 8 years, we can start with the initial amount of $1000 and increase it by 8% each year.
Year 1: $1000 + 8% = $1080
Year 2: $1080 + 8% = $1166.40
Year 3: $1166.40 + 8% = $1259.71
Year 4: $1259.71 + 8% = $1359.85
Year 5: $1359.85 + 8% = $1467.99
Year 6: $1467.99 + 8% = $1584.47
Year 7: $1584.47 + 8% = $1710.69
Year 8: $1710.69 + 8% = $1847.01
So the sequence describing the amount of money in Nico's savings account each year for 8 years is: $1000, $1080, $1166.40, $1259.71, $1359.85, $1467.99, $1584.47, $1710.69, $1847.01.