7.4 Exponential Functions

3 practice questionsNot yet reviewed

Notes

An exponential function has the form $f(x) = a \cdot b^x$ with $a \ne 0$, $b > 0$ and $b \ne 1$.

$a$ is the initial value (the $y$-intercept). $b$ is the growth factor: each time $x$ increases by 1, the output is multiplied by $b$.
If $b > 1$ the function grows; if $0 < b < 1$ it decays.
In a table, equal steps in $x$ give a constant ratio of outputs (linear functions have a constant difference).

What is the $y$-intercept of $f(x) = 5 \cdot 3^x$?

Which table is exponential? ($x$ = 0, 1, 2, 3)

$g(x) = 200(0.5)^x$. What is $g(3)$?