An initial investment of $60.00 increases in value by 15% each year. Which of the following statements are true? Select all that apply. Round your answers to the nearest dollar.
Π This situation can be represented by the quadratic function f(x) = 0.15(x+60)2.
Π
This situation can be represented by the exponential function f(x) = 60.1.15*.
This function has no x-intercept.
After 4 years, the value of the investment will be $120.00.
After 6 years, the value of the investment will be $653.00.
After 7.86 years, the value of the investment will be about 3 times the initial value.
After 8 years, the value of the investment will be $184.00.
explain the answer
The correct statements are:
- This situation can be represented by the exponential function f(x) = 60.1.15x.
- After 4 years, the value of the investment will be $120.00.
- After 6 years, the value of the investment will be $653.00.
The growth of the investment is exponential, not quadratic. The formula for exponential growth is given by f(x) = initial value * (1 + growth rate)^(number of years). In this case, the initial value is $60.00, the growth rate is 15% or 0.15, and the number of years is x.
After 4 years, the calculation would be f(4) = 60.00 * (1 + 0.15)^4 = 120.00, so the value of the investment would be $120.00 after 4 years.
After 6 years, the calculation would be f(6) = 60.00 * (1 + 0.15)^6 ≈ 653.03, so the value of the investment would be approximately $653.00 after 6 years. This shows that the value is growing exponentially.
Therefore, the exponential function correctly models the situation, and the values after 4 and 6 years are accurately calculated.