QUES $24\mathrm{.}11$

$24\mathrm{.}11$ Glaucoma is the second leading cause of vision loss worldwide. High intraocular pressure $($pressure inside the eye$)$ almost always accompanies vision loss. It is postulated that the high pressure damages a subset of cells in the eye that are responsible for vision. One investigator theorizes that the relationship between vision loss and pressure can be described as

$VL=$Aexp$(k{\displaystyle \underset{25}{\overset{t}{}}}(P-13)dt)$

where $VL$ is percent vision loss, $P$ is intraocular pressure $(mmHg),t$ is time $($years$),$ and $k$ and A are constants. Using the data below from three patients, estimate the constants $k$ and $A.$

$\backslash$table$[[$Patient$,$A$,$B$,$C$],[\backslash$table$[[$Age at diagnosis$],[$VL$]],\backslash$table$[[65],[60]],\backslash$table$[[43],[40]],\backslash$table$[[80],[30]]],[$Age$,$ years,P$,$mmHg$,$Age, years,P$,$mmHg$,$Age, years,P$,$mmHg$],[\backslash$table$[[25],[40],[50],[60],[65]],\backslash$table$[[13],[15],[22],[23],[24]],\backslash$table$[[25],[40],[41],[42],[43]],\backslash$table$[[11],[30],[32],[33],[35]],\backslash$table$[[25],[40],[50],[60],[80]],\backslash$table$[[13],[14],[15],[17],[19]]]]$