You pay off a debt of $800 by paying 24% of the remaining balance each month. Find a formula that gives the remaining debt D after t months.

Question

The answer starts with B=   I can not figure this out

Answer 1

This is an exponential decay situation.  At the end of each month, the debt is (100-24)% of what it was at the start of the month, which is 0.76 times what it was at the start of the month.  Keep this up for t months and get

 

D(t) = D₀ (0.76)^t,

 

where 

 

D₀ = initial debt of $800

t = number of months elapsed since the debt was $800

 

D(t) = 800 (0.76)^t