Question

If the original cost of a TV is 1250.00 but decreases by 4.5% each week, how many weeks before the TV will cost 800.00?

Answer 1

This is exponential growth/decay type problem...

F=Ir^t, F=final value, I=initial value, r=rate, t=time, in this case I=1250 and r=(1-.045)=0.955 so

F=1250(.955)^t  and we want to find t for when F=800 

800=1250(.955)^t

.64=.955^t  take the natural log of both sides...

ln.64=t ln.955

t=(ln.64)/ln.995

t≈9.69 weeks

t≈9.69 weeks (to nearest hundredth of a week)

Answer 2

800=1250(1-0.045)^t
Solve for t
t=log(800÷1,250)÷log(1−0.045)
t=9.7 weeks

Check
A=1,250×(1−0.045)^(9.7)
A=799.7=800