Question 544013
Well since we're trying to find how much she saves each week, let's look to see what pattern forms:
{{{Week1 = 20}}}
{{{Week2 = 20*1.10 = 22}}}
{{{Week3 = 22*1.10 = (20*1.10)*1.10 = 20*(1.10^2) = 24.20}}}
{{{Week4 = 24.20*1.10 = (20*1.10*1.10)*1.10 = 20*(1.10^3) = 26.62}}}
Have you spotted the pattern yet? It's always {{{20*(1.10^x)}}} where the exponent is always the # of the week, minus 1. (Week2 was {{{20*(1.10^1)}}})
.
So use the following formula:
{{{A=p*(1.10)^(n-1)}}}
"A" = amount saved
"p" = initial amount
"n" = number of weeks
.
So for instance, week 1:
{{{A=p*(1.10)^(n-1)}}}
{{{A=20*(1.10)^(1-1)}}}
{{{A=20*(1.10)^(0)=20*1=20}}}
.
Or week 4:
{{{A=p*(1.10)^(n-1)}}}
{{{A=20*(1.10)^(4-1)}}}
{{{A=20*(1.10)^(3)=20*1.331=26.62}}}
.
Both of which we know to be true from our examples above. But now you know how to calculate week 7, 17, or 700 (if needed). Hope this helps!