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Math·Advanced Math·Nonlinear functions

hard

A model estimates that in a particular forest, the number of trees with any given diameter measured at shoulder height is $21\%$ less for each $1$-inch increase in tree diameter measured at shoulder height. The model can be written in the form $f(x)=a(b{)}^x$, where $a$ and $b$ are constants and $x$ is the tree’s diameter, in inches, measured at shoulder height, and $x\ge 5$. The model estimates that $3,100$ trees in this forest have a diameter of $13$ inches measured at shoulder height. Which function best represents this model?

A

$f(x)=3,100(0.21{)}^x$

B

$f(x)=3,100(0.79{)}^x$

C

$f(x)=66,000(0.21{)}^x$

D

$f(x)=66,000(0.79{)}^x$