A national census bureau predicts that a certain population will increase from

$31\mathrm{.}431\mathrm{.}4$

million in $2000$ to

$56\mathrm{.}556\mathrm{.}5$

million in

$20802080.$

Complete parts$($a$)$ through$($c$).$

Question content area bottom

Part $1$

$($a$)$ Find an exponential function of the form

$$f$($t$)$equals$=$y $0$ b Superscript ty$0$bt

for these$$ data, in which

tequals$=0$

corresponds to $2000$ and$$ f$($t$)$ is in millions.

$$f$($t$)$equals$=31\mathrm{.}4$ x left parenthesis $1\mathrm{.}0074$ right parenthesis Superscript

$($Use integers or decimals for any numbers in the expression. Round to four decimal places as$$ needed.$)$