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. 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.
The money in Nico's savings account over time is an example of exponential growth because the amount of money is increasing by a constant percentage (8%) each year.
To create a sequence that describes the amount of money in Nico's savings account each year for 8 years, we can use the formula y = a⋅b^x, where a is the initial amount ($1000), b is the growth factor (1.08), and x is the number of years.
Year 1: y = $1000 * (1.08)^1 = $1080
Year 2: y = $1000 * (1.08)^2 = $1166.40
Year 3: y = $1000 * (1.08)^3 = $1259.71
Year 4: y = $1000 * (1.08)^4 = $1360.49
Year 5: y = $1000 * (1.08)^5 = $1470.90
Year 6: y = $1000 * (1.08)^6 = $1589.85
Year 7: y = $1000 * (1.08)^7 = $1718.63
Year 8: y = $1000 * (1.08)^8 = $1857.64
To find the amount of money in Nico's savings account after 18 years, we can use the formula y = a⋅b^x, where a is the initial amount ($1000), b is the growth factor (1.08), and x is the number of years.
y = $1000 * (1.08)^18 = $2949.08
Therefore, the amount of money in Nico's savings account after 18 years is $2949.08.