Question
$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 f(x)=1000(b)^x, where f(x) is the amount in the savings account, and x is time in years. What is the value of b?
A. 0.60
B. 1.02
C. 0.80
D. 1.04
A. 0.60
B. 1.02
C. 0.80
D. 1.04
Answers
GPT 3.5
D. 1.04
To find the value of b, we can plug in the values from the scenario into the exponential function:
For 1 year: 1020 = 1000(b)^1
Solving for b, we get b = 1.02
For 2 years: 1040.40 = 1000(b)^2
Substitute b = 1.02 into the equation:
1040.40 = 1000(1.02)^2
1040.40 = 1000(1.0404)
Therefore, the value of b is 1.04.
To find the value of b, we can plug in the values from the scenario into the exponential function:
For 1 year: 1020 = 1000(b)^1
Solving for b, we get b = 1.02
For 2 years: 1040.40 = 1000(b)^2
Substitute b = 1.02 into the equation:
1040.40 = 1000(1.02)^2
1040.40 = 1000(1.0404)
Therefore, the value of b is 1.04.