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Question 1207165: Chris has invented a new app for smart phones that two companies are interested in purchasing for a 2-year contract.
Company A is offering her $10,000 for the first month and will increase the amount each month by $5000.
Company B is offering $500 for the first month and will double their payment each month from the previous month.
Monthly payments are made at the end of each month. For which monthly payment will company B’s payment first exceed company A’s payment?
A. 6
B. 7
C. 8
D. 9
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Chris has invented a new app for smart phones that two companies are interested in purchasing for a 2-year contract.
Company A is offering her $10,000 for the first month and will increase the amount each month by $5000.
Company B is offering $500 for the first month and will double their payment each month from the previous month.
Monthly payments are made at the end of each month. For which monthly payment will company B’s payment first exceed company A’s payment?
Company A is offering her $10,000 for the first month and will increase the amount each month by $5000.
Every month there is an increase of $5000. (fixed)
We use a(n) formula of arithmetic squence.
Let n be the number of months when salary of B greater than that of A
a(n)= 10000+ (n-1)*5000
a(n) = 10000+5000n-5000 = 5000+5000n
Company B is offering $500 for the first month and will double their payment each month from the previous month.
Here it forms a geometric sequence with ratio r=2
a=500
a(n) = 500*2^(n-1)
500*2^(n-1) >5000+5000n
2^(n-1) >10+10n
Find n using calculator to find when B's salary will be higher than A's
or plug n = 5,6,7,8,9 to find the correct choice
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