8. Suppose an investment of $5,000 doubles every 12
years. How much is the investment worth after 36
years? After 48 years?
Write and solve an exponential equation.
5000 * 2^(n/12)
its not so confusing. just multiply 2 to 5,000 then then again and agin and again. you will need to do this 4 times. 5,000*4=20,000
How do I write and solve an exponential equation though?
To find out how much the investment is worth after 36 years and 48 years, we can use the exponential equation formula:
A = P * (1 + r)^t
Where:
A is the amount after time t
P is the initial amount
r is the rate of growth (expressed as a decimal)
t is the time period in years
In this case, the initial amount (P) is $5,000 and it doubles every 12 years. To express this as a rate of growth (r), we divide the doubling time by the time period:
r = 1/12
Now we can calculate the worth of the investment after 36 years:
A = 5000 * (1 + 1/12)^36
Simplifying the equation:
A = 5000 * (13/12)^36
To solve this exponential equation, you can either use a calculator or a mathematical software like Python, MATLAB, or Excel. I will use a calculator to find the value:
A ≈ 5,000 * (13/12)^36
A ≈ 5,000 * (2.13599)^36
A ≈ 5,000 * 4.31311
A ≈ $21,565.57
Thus, the investment will be worth approximately $21,565.57 after 36 years.
Now let's calculate the worth after 48 years:
A = 5000 * (1 + 1/12)^48
Simplifying the equation:
A = 5000 * (13/12)^48
Using a calculator:
A ≈ 5,000 * (13/12)^48
A ≈ 5,000 * (2.80834)^48
A ≈ 5,000 * 123.2006
A ≈ $616,002.93
Therefore, the investment will be worth approximately $616,002.93 after 48 years.