HA2 6.1-6.3 practice 3

Match the letter of the correct graph for each function.

(A) [math]y=2^{x+3}[/math]
(B) [math]y=2^{x-3}[/math]
(C) [math]y=2^x+3[/math]
(D) [math]y=2^x-3[/math]

(a) Which function equation above represents [math]g(x)[/math]?

(b) Which function equation above represents [math]h(x)[/math]?

(Calculator) In the half-life formula [math]A(t)[/math], [math]h[/math] is the half-life of the substance, [math]A_0[/math] is the starting (initial) amount the substance, and [math]A(t)[/math] is the amount of the substance remaining after time, [math]t[/math]. The half-life of Carbon-14 is 5,743 years. How long would it take for a fossil that originally had 200 grams of Carbon-14 to decay to 70 grams? (Integer)

(Calculator) Exponential growth of investments can be modeled with the following equation: [math]A=P(1+\displaystyle{\frac{r}{n}})^{nt}[/math]. In this equation, [math]r[/math] is the annual interest rate, [math]n[/math] is the number of compounding periods per year, [math]P[/math] is the principal (original amount invested), [math]A[/math] is the amount of the investment after [math]t[/math] years. Years ago, hoping to retire some day, Mr. Uhlman invests $50,000 into an account earning 9% interest, compounded monthly. How long will it take for his investment to grow to $1,000,000? (1 decimal place)

Solve [math]\displaystyle{\left(\frac{1}{2}\right)^x}=\displaystyle{\frac{1}{32}}[/math]

Solve [math]\displaystyle{(e^x)^2}=\displaystyle{\frac{e^{3x}}{e^2}}[/math]

Find the summation of the solutions to the equation [math]5^{x^2-4}=125^x[/math]

Find the noninteger solutions to the equation [math]9^{2x}\cdot27^{x^2}=3^{-1}[/math]

Solve [math]2^{x+5}-2^{x+3}=6[/math]

Solve [math]3^{2x}-7\cdot(3)^x-18=0[/math]

Find the product of the solutions to the equation [math]4^x-33\cdot2^{x-1}+8=0[/math]