The amount spent by a consumer on nondurable goods can be modeled as

$n(x)=-1\mathrm{.}1+1\mathrm{.}64lnx$ thousand dollars

and the amount spent on motor vehicles can be modeled as

$m(x)=1\mathrm{.}62({1\mathrm{.}26}^x)$ hundred dollars

where $x$ thousand dollars is the amount spent by that same consumer for all personal consumption. $+($Note: Use the concept of inverse functions or models.$)$

where $m$ is the amount spent on motor vehicles. $($Round all numerical values to three decimal places.$)$

$x(m)=4\mathrm{.}327ln(m)-2\mathrm{.}087,$ thousand dollars

$n(x(m))=1\mathrm{.}64ln(|4\mathrm{.}327ln(m)-2\mathrm{.}087|)-1\mathrm{.}1,$ thousand dollars

$($c$)$ How much is spent on nondurable goods by somebody who spends $$350$ on his or her motor vehicle? $($Round your answer to three decimal places.$)$

$

$x$ thousand

At what rate is this amount changing with respect to motor vehicle spending? $($Round your answer to three decimal places.$)$

$

thousand per hundred dollars

Write a sentence of interpretation for the results.

A consumer who spends $$350$ on his or her motor velles w $

thousand on nondurable goods. At the $$350$ level of spending on motor vehicles, the amount spent on nondurable goods is increasing $$

by $

thousand per hundred dollars increase in spending on motor vehicles.