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?
After 2 years i got, 6107.01. Is that right?
For 2 years not quite. (I used a interest calculator to check my answer.)
So the interest rate is 10%
So to calculate what you need to multiply the starting principle (the starting money) by do 1.10^2 (1.10 represents the intrest rate) (2 represents the years/how many times its compounded)
That should give you 1.21
Then multiply (1.12)(5000)
that will give you 6,050
For 10 years replace the years to 10
12,968.7
so, 5000*1.10^x is the model equation, right?
and what type of exponential model is it?
Natalie's situation can be modeled using the exponential growth model, specifically the continuous compounding formula.
The model equation for Natalie's situation can be written as:
A = P * e^(rt)
Where:
A represents the total amount of money after a specified time period,
P represents the principal amount (initial investment),
e represents the mathematical constant approximately equal to 2.71828,
r represents the interest rate (in decimal form),
t represents the time period (in years).
In this case, Natalie's initial investment (P) is $5000, the interest rate (r) is 10% or 0.10, and t represents the number of years.
To calculate how much money Natalie will have after 2 years, we substitute the values into the equation:
A = 5000 * e^(0.10 * 2)
A = 5000 * e^(0.20)
A ≈ 5000 * 1.22140
A ≈ $6107.01
So it appears you calculated the amount correctly. Natalie will have approximately $6,107.01 after 2 years.
To find out how much money Natalie will have after 10 years, we use the same formula:
A = 5000 * e^(0.10 * 10)
A = 5000 * e^(1.0)
A ≈ 5000 * 2.71828
A ≈ $13,591.40
Therefore, after 10 years, Natalie will have approximately $13,591.40.