$1,000 is deposited into a savings account. Interest is compounded annually. After 1 year, the value of the account is $1,020. After 2 years, the value of the account is $1,040.40. This scenario can be represented by an exponential function of the form , where is the amount in the savings account, and is time in years. What is the value of b?
To find the value of b in the exponential function, we need to use the given information to set up and solve a system of equations.
From the information provided:
- After 1 year, the value of the account is $1,020. This can be represented as:
- After 2 years, the value of the account is $1,040.40. This can be represented as:
From the first equation, we get:
$1,020 = a \times b^1
From the second equation, we get:
$1,040.40 = a \times b^2
Now we can divide the second equation by the first equation to eliminate a:
$1,040.40 / $1,020 = b^2 / b^1
1.02 = b
Therefore, the value of b is 1.02.