13. Let A = the amount of money in the given time, P = principal amount; the amount of money you start with, T = time in years, R = interest rate, and N = amount of times interest is compounded each year.
The formula for compound interest is:
[tex]A = P(1 + \frac{R}{N} )^{NT} [/tex]
Now, we find in the information from the description needed to plug in. P = $1000, R = 7% or 0.07, N = 1 time a year, T = 3 years
[tex]A = 1000(1 + \frac{0.07}{1})^{1(3)} [/tex]
This simplifies to:
[tex]A = 1000(1 + 0.07)^{3} [/tex]
And again to:
[tex]A = 1000(1.07)^{3} [/tex]
Plug this into a calculator:
A = 1225.043 or ≈1,225.04
14. (x² + 3)(x - 3)(x + 3)
I'm going to do FOIL method on the second and third binomials first and simplify. This gives you:
(x² + 3)(x² - 9)
Then you do the FOIL method again to get:
x⁴ - 9x² + 3x² - 27
And combine like terms for your answer:
x⁴ - 6x² - 27
Number 15 doesn't give you a number to set the polynomial (that results from multiplying those two binomials) equal to so I'm guessing it wants you to set said polynomial equal to zero and solve for x then plug back in.
If not, your area is found by the equation 3x² - 5x - 12
