Mia deposits $500 into a savings account. The table below shows the amount of money in her account over time. x represents the time in years since her initial deposit and y represents the amount of money in her account.
x 0 1 2 3 4
y 500 550 605 665.5 732.05
Write a linear, quadratic, or exponential function to represent the data, then find approximately how much money will be in her account after 6 years.
(1 point)
Responses
$800.00
$800.00
$805.26
$805.26
$865.15
$865.15
$885.78
The data appears to be following an exponential function.
The formula for an exponential function is y = a * (1 + r)^x, where:
- y is the amount of money in the account
- a is the initial deposit ($500)
- r is the growth rate
- x is the time in years
Using the data provided:
- When x = 0, y = 500
- When x = 1, y = 550
- When x = 2, y = 605
- When x = 3, y = 665.5
- When x = 4, y = 732.05
Substitute the values into the formula:
500 = a * (1 + r)^0 --> a = 500
550 = 500 * (1 + r)^1 --> (1 + r) = 1.1 --> r = 0.1 (growth rate)
605 = 500 * (1.1)^2
665.5 = 500 * (1.1)^3
732.05 = 500 * (1.1)^4
Now, to find how much money will be in her account after 6 years (x = 6):
y = 500 * (1.1)^6 ≈ $803.85
So, approximately $803.85 will be in her account after 6 years.