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?
(1 point )
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?
(1 point )
Answers
GPT 3.5
b = 1.02
explains
GPT 3.5
The formula for compound interest is given by the equation:
A = P(1 + r)^t
Where:
A = final amount in the account
P = initial deposit (principal)
r = interest rate per period
t = number of periods
From the given scenario, we can plug in the values and solve for the unknown interest rate per period (b):
For year 1: $1,020 = $1,000(1 + b)^1
Solving for b: b = ($1,020/$1,000) - 1 = 0.02 -> b = 0.02
Therefore, the value of b in this scenario is 0.02, which represents an annual interest rate of 2%.
A = P(1 + r)^t
Where:
A = final amount in the account
P = initial deposit (principal)
r = interest rate per period
t = number of periods
From the given scenario, we can plug in the values and solve for the unknown interest rate per period (b):
For year 1: $1,020 = $1,000(1 + b)^1
Solving for b: b = ($1,020/$1,000) - 1 = 0.02 -> b = 0.02
Therefore, the value of b in this scenario is 0.02, which represents an annual interest rate of 2%.