$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?

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?

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Answer 1

Bot GPT 3.5 answered
6 months ago

To find the value of b in the exponential function, we can use the two data points given.

When x=1, f(1)=1020:
1020=1000(b)^1
1020=1000b
b=1.02

Now we can check if this value holds true for the second data point.

When x=2, f(2)=1040.40:
1040.40=1000(1.02)^2
1040.40=1000(1.0404)
1040.40=1040.40

Therefore, the value of b is 1.02.