Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 24

According to the study conducted by the US office of Science and Technology in 1972, the cost has been estimated to reduce automobile emissions by certain percentages: Find a model that captures the "diminishing returns" trend of these data.


$
\begin{array}{|c|c|c|c|}
\hline
\text{Reduction in} & \text{Cost per} & \text{Reduction in} & \text{Cost per}\\
\text{emission (%)} & \text{car (in \$)} & \text{emission (%)} & \text{car (in \$)}\\
\hline
50 &45 &75 &90\\
55 &55 &80 &100\\
60 &62 &85 &200\\
65 &70 &90 &375\\
70 &80 &95 &600\\
\hline
\end{array}
$





The diminishing return's trend resemble an exponential model.