- This situation can be represented by the exponential function f(x)=60 x 1.15^x
- After 4 years the value of the investment will be $120.00
- After 8 years the value of the investment will be $184.00
An initial investment of $60.00 increases in value by 15% each year. Which of the following statements are true? Select all that apply.
Select answers;
This function can be represented by the quadratic equation f(x)=0.15(x+60)^2
This situation can be represented by the exponential function f(x)=60 x 1.15^x
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 3 times the initial value
After 8 years the value of the investment will be $184.00
5 answers
2,3,6,7 correct
Thank you for confirming.
how to get them
To determine which statements are true, we can analyze the given information about the investment increasing in value by 15% each year.
1. This situation can be represented by the exponential function f(x)=60 x 1.15^x: This is true because the exponential function represents continuous growth, which aligns with the scenario of the investment increasing by 15% each year.
2. This function has no x-intercept: This is true because the exponential function f(x)=60 x 1.15^x will never reach zero, indicating there is no x-intercept.
3. After 4 years, the value of the investment will be $120.00: This is true because after 4 years, the value of the investment can be calculated by plugging x=4 into the exponential function f(x)=60 x 1.15^x, which equals $120.00.
4. After 6 years, the value of the investment will be $653.00: This is false. To verify, you can calculate the value after 6 years by plugging x=6 into the exponential function f(x)=60 x 1.15^x, which equals $208.98, not $653.00.
5. After 7.86 years, the value of the investment will be 3 times the initial value: This is true. You can calculate the value after 7.86 years by plugging x=7.86 into the exponential function f(x)=60 x 1.15^x, which equals $180.72, approximately 3 times the initial value of $60.
6. After 8 years, the value of the investment will be $184.00: This is true. You can calculate the value after 8 years by plugging x=8 into the exponential function f(x)=60 x 1.15^x, which equals $183.57. This is closest to $184.00 among the given options.
1. This situation can be represented by the exponential function f(x)=60 x 1.15^x: This is true because the exponential function represents continuous growth, which aligns with the scenario of the investment increasing by 15% each year.
2. This function has no x-intercept: This is true because the exponential function f(x)=60 x 1.15^x will never reach zero, indicating there is no x-intercept.
3. After 4 years, the value of the investment will be $120.00: This is true because after 4 years, the value of the investment can be calculated by plugging x=4 into the exponential function f(x)=60 x 1.15^x, which equals $120.00.
4. After 6 years, the value of the investment will be $653.00: This is false. To verify, you can calculate the value after 6 years by plugging x=6 into the exponential function f(x)=60 x 1.15^x, which equals $208.98, not $653.00.
5. After 7.86 years, the value of the investment will be 3 times the initial value: This is true. You can calculate the value after 7.86 years by plugging x=7.86 into the exponential function f(x)=60 x 1.15^x, which equals $180.72, approximately 3 times the initial value of $60.
6. After 8 years, the value of the investment will be $184.00: This is true. You can calculate the value after 8 years by plugging x=8 into the exponential function f(x)=60 x 1.15^x, which equals $183.57. This is closest to $184.00 among the given options.
1 answer