Question

Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.

Miguel had $25 in his savings account. His parents will double the amount in his account each month.

If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.

Answer 1

Anita

Answer 2

for Anita
Amount=400+200x
for Miguel
\[Amount=25(2)^x\]
Miguel account increases exponentially
so it increases faster.
\[400+200x=25(2)^x\]
divide by 25
\[16+8x=2^x\]
for x=6
\[16+8*6=2^6\]
\[16+48=64\]
64=64
after 6 months amount will be similar and afterwards Miguel amount will be more.
you can see it in the following table.

where x is the number of months

number of months Anita Miguel
x
______________________________________
1 600 50
2 800 100
3 1000 200
4 1200 400
5 1400 800
6 1600 1600
7 1800 3200
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