Exponential Function Properties
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Problems 16
- Do y=(12 )−xy=(\frac{1}{2}\ )^{-x}y=(21 )−x and y=2xy=2^xy=2x have the same graph?
- If 2x=y2^x = y2x=y for some real numbers xxx and yyy, then what is 8x8^x8x in terms of yyy?
- Let a,b,c∈Ra,b,c \in \mathbb{R}a,b,c∈R. Which of the following are true about exponentiation?
- Let aaa be a real number and consider the function f(x)=(a5−2)xf(x) = (\frac{a}{5}-2)^xf(x)=(5a−2)x. If fff is an exponential decay function, what interval must aaa be in?
- Which family is the function f=(−2)xf = (-2)^xf=(−2)x in?
- Which family is the function f(x)=72xf(x) = 7^{2x}f(x)=72x in?
- What is e2x⋅e3xe^{2x} \cdot e^{3x}e2x⋅e3x?
- Solve for xxx. ex−5⋅ex−1=e−4e^{x-5} \cdot e^{x-1} = e^{-4}ex−5⋅ex−1=e−4
- Let yyy be a positive rational number. If x>1x > 1x>1, what is the smallest value of xxx such that xyx^yxy is an integer?
- If z=3xz=3^xz=3x and y=z2y=z^2y=z2 what is the relation between yyy and xxx?
- If z=2⋅5xz=2\cdot5^xz=2⋅5x and y=z3y=z^3y=z3 what is the relation between y and x?
- True or False\text{True or False}True or False === Consider the exponential mnm^nmn If the integer base of an exponential is increased by 1, then the exponential is then increas…
- Which of the following is equivalent to f(x)=ex2f(x)=e^{x^2}f(x)=ex2?
- Solve the following system of equations: {y=ex2+6x+8y=e2x+4\begin{cases}y=e^{x^2+6x+8}\\y=e^{2x+4} \end{cases}{y=ex2+6x+8y=e2x+4
- An exponential function is defined as f(x)=(52a−3)xf(x)=(\frac52 a-3)^xf(x)=(25a−3)x. What interval must aaa fall under for this function to show exponential growth?
- Your car's monetary value is modeled by the following function: y=10000(1−.2)xy=10000(1-.2)^xy=10000(1−.2)x Does this show exponential growth or exponential decay?