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.
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.
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