Natalie has $5000 and decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.
What type of exponential model is Natalie’s situation?
Write the model equation for Natalie’s situation
How much money will Natalie have after 2 years?
How much money will Natalie have after 10 years?
Exponential function where
Amount = 5000 e^(.1t)
replace t with 2 and with 10
let me know what you got for "after 2 years" to make sure your getting it correct
5000 * e^0.10x
see what you can do with that
Natalie's situation can be modeled using the continuous compound interest formula. This is an exponential growth model.
The model equation for Natalie's situation is given by the formula:
A = P * e^(rt)
Where:
A = the final amount after time t
P = the initial principal (starting amount)
e = Euler's number (approximately 2.71828)
r = the interest rate (as a decimal)
t = time (in years)
In Natalie's case, the starting amount (principal) is $5000 and the interest rate is 10% or 0.10. We need to find out how much money she will have after 2 years and 10 years.
For 2 years:
A = 5000 * e^(0.10 * 2)
To calculate this, we need to use the value of e raised to the power of (0.10 * 2). This can be done using a calculator, or you can use the approximation e^x ≈ 1 + x if the value of x is small. In this case, we have (0.10 * 2) = 0.20, which is small. So we can approximate e^(0.20) as approximately 1 + 0.20, which equals 1.20.
A ≈ 5000 * 1.20
A ≈ $6000
After 2 years, Natalie will have approximately $6000.
For 10 years:
A = 5000 * e^(0.10 * 10)
Again, we need to calculate e^(0.10 * 10). This value is not as small, so we'll use a calculator to get the precise value.
A ≈ 5000 * 2.71828^(0.10 * 10)
A ≈ 5000 * 2.71828^1
A ≈ 5000 * 2.71828
A ≈ $16487.06
After 10 years, Natalie will have approximately $16487.06.
i got 6107.01
is that right?