Question

Mike and Anna invested money into two different accounts. The function f(x) = 8,500(1.08)* models the

amount in Mike's account after x years. The table of values below shows the amount in Anna's account after x
years.
O
O
Anna's Account
The total amount in Anna's account is modeled with an exponential best-fit function. Which statement best
describes the two accounts?
OA Mike initially invested about $1,300 more than Anna.
O
Number of
Years
(x)
5
8
11
14
Value of
Account
g(x)
$9,818
$12,027
$14,734
$18,050
B. Mike initially invested about $700 more than Anna.
C. Mike initially invested about $2,300 more than Anna.
D. Mike initially invested about $1,500 more than Anna.

Answer 1

The function for Mike's account is f(x) = 8,500(1.08)^x. We do not have the initial amount invested by Anna, but we can use the table of values to find the growth rate of her account.

Using the values in the table, we can find that the growth rate is approximately 1.103. So, the exponential function for Anna's account is g(x) = a(1.103)^x, where a is the initial amount invested by Anna.

To compare the initial amounts invested by Mike and Anna, we can set up the equation f(0) = g(0) and solve for a:

f(0) = g(0)

8,500(1.08)^0 = a(1.103)^0

8,500 = a

So, Anna initially invested $8,500.

Now, we can compare the initial amounts invested by Mike and Anna:

Mike's initial investment = $8,500

Anna's initial investment = $8,500

Therefore, statement A is false, statement B is false, statement C is false, and the correct answer is statement D.