SOLUTION: Kendall is planning to buy a laptop for 1200 each month she doubles the amount she saved the previous month.If she saves $20 the first month in how many months will Kendall have e

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Kendall is planning to buy a laptop for 1200 each month she doubles the amount she saved the previous month.If she saves $20 the first month in how many months will Kendall have e      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 788593: Kendall is planning to buy a laptop for 1200 each month she doubles the amount she saved the previous month.If she saves $20 the first month in how many months will Kendall have enough money to buy the laptop

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Amount saved each month:
1st month: 20
2nd month: 2*20
3rd month: 4*20
4th month: 8*20
etc.
Summing up the amounts saved:
+20+%2B+2%2A20++4%2A20+%2B+8%2A20+ etc,.
+20%2A%28+1+%2B+2+%2B+4+%2B+8+%29+ etc.
+20%2A%28+2%5En+-+1+%29+
where +n+ is the number of months
given:
+20%2A%28+2%5En+-+1+%29+=+1200+
+2%5En+-+1+=+60+
+2%5En+=+61+
Take log base 10 of both sides
+n%2Alog%282%29++=+log%2861%29+
+.301n+=+1.785+
+n+=+5.931+
She will have enough money in about 6 months
check:
+20%2A%28+1+%2B+2+%2B+4+%2B+8+%2B+16+%2B+32+%29+=+20%2A63+
+20%2A63+=+1260+
At the end of only 5 months, she has:
+20%2A%28+1+%2B+2+%2B+4+%2B+8+%2B+16+%29+=+20%2A31+
+20%2A31+=+620+
OK