Exponents, Radicals, and Exponential Functions

If f(x) = 2^x , which of the following is the graph of

g(x) = f(x) + 2

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What is the equivalent expression in exponential form?

•  $224^{\frac{1}{5}}r^{\frac{1}{35}}$  

•  $224r^{\frac{5}{7}}$  

•  $\left(224r\right)^{\frac{7}{5}}$  

•  $\left(224r^7\right)^{\frac{1}{5}}$  

Simplify in Exponential Form.

• $\left(2^{\frac{1}{20}}\right)$

• $2^{\frac{4}{5}}$

• $\left(2^5\right)^4$

• $2^{\frac{5}{4}}$

Write in radical form.

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Simplify

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Simplify

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If a city with a population of 15,000 doubles in size every year, what will the population be 8 years from now?

The compact disc, CD, has been declining in popularity each year.  One executive has predicted the sales can be represented by the following function. $f\left(t\right)=13,000,000\left(0.80\right)^t$  

Select ALL that are TRUE.

• This is an exponential growth function.

• This is an exponential decay function.

• The sales in CDs are decreasing by 20% each year..

• The sales in CDs are increasing by 80% each year.

The functions $f\left(x\right)=x+2\ and\ g\left(x\right)=2^x-3$  

are graphed.  What are the solutions, to the nearest integer, for f(x)=g(x)?

• 5 and -3

• 3 and -5

• 2 and -2

• -10 and 6