Sam borrows $$20,000$ from a bank at an interest rate of $7\%$ and pays back the loan continuously at a rate of N dollars$/$year$.$ Let P$($t$)$ denote the amount still owed at time t$.($a$)$ Does P$($t$)$ satisfy the differential equation y$=0\mathrm{.}07$y$$N$?$

A$.$ yes

B$.$ no

$($b$)$ How long will it take Sam to pay back the loan if N$=$$$1,800?$

It will take Sam approximately years to pay back the loan.

Answer to the nearest whole year.$($c$)$ Will he ever be able to pay back the loan if N$=1300$ dollars?

A$.$ no

B$.$ yes