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?

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

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)