Question

Delilah makes an investment of $10,000 at 7% annual interest and wants to wait until it reaches $15,500 before withdrawing her investment.

Write an exponential equation that represents this situation where x represents years.

What problems do you run into trying to solve an equation like this?

Answer 1

Explanation:

We can see that Delilah makes an investment of 10,000 we divided by 7% which gives us 700 we times that by 7 which gives us 4900 then we multiply by 1.12 which give us 7 years and 43.8 days.

Answer 2

15,500 = 10,000(1 + 0.07)^x

Explanation:

The exponential equation that represents this situation is:

15,500 = 10,000(1 + 0.07)^x

In this equation, the initial investment of $10,000 is multiplied by the factor (1 + 0.07)^x, which represents the growth of the investment at an annual interest rate of 7%. The variable x represents the number of years that the investment has been growing.

To solve this equation for x, we need to use logarithms to isolate the exponent:

log(1 + 0.07)^x = log(15,500/10,000)

x * log(1 + 0.07) = log(1.55)

x = log(1.55) / log(1 + 0.07)

x ≈ 7.85 years

One potential problem with this type of equation is that it assumes a constant interest rate and continuous compounding, which may not be the case in real-world situations. In addition, there may be other factors that affect the growth of the investment, such as taxes or fees, which are not accounted for in this equation.