Exponential Functions flashcards

Question 1

What is an exponential function?

Accepted Answer

A function where the variable is in the exponent, typically written $f(x)=a\,b^x$ with $a
eq 0$, $b>0$, and $b
eq 1$.

Question 2

State the compound interest formula with $n$ compounds per year.

Accepted Answer

$$A=P\left(1+\frac{r}{n}\right)^{nt}$$ where $P$ is principal, $r$ is annual interest rate (decimal), $n$ is compounds per year, and $t$ is years.

Question 3

How do you graph $f(x)=a\,b^x+c$ using transformations?

Accepted Answer

Graph $y=b^x$, then vertically stretch by $|a|$ (reflect over the $x$-axis if $a<0$), and shift up/down by $c$.

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