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
$805.26
$865.15
$885.78
To represent the data in the table, we can see that the amount in Mia's account is increasing over time. This indicates that it is an exponential function.
The general form of an exponential function is y = a * b^x, where 'a' is the initial amount and 'b' is the growth factor.
From the table:
When x = 0, y = 500
y = a * b^0
500 = a
Now we can find the growth factor 'b':
When x = 1, y = 550
550 = 500 * b^1
550 = 500b
b = 1.1
Therefore, the exponential function representing the data is:
y = 500 * 1.1^x
To find approximately how much money will be in her account after 6 years:
y = 500 * 1.1^6
y ≈ 805.26
Therefore, after 6 years, there will be approximately $805.26 in Mia's account.
The correct answer is $805.26.