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If the price of coffee, p, doubles every week for 4 weeks

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by BTGmoderatorDC » Mon Mar 12, 2018 9:37 pm
If the price of coffee, p, doubles every week for 4 weeks, triples a week later, and finally quadruples a week after that, which of the following represents the price of coffee at the end of period, in terms of p?

A. 15p
B. 7*8*p
C. 7*2^4*p
D. 3*4*8*p
E. 12*2^4*p

Can some experts help me solve this problem?

OA E
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by ErikaPrepScholar » Tue Mar 13, 2018 5:56 am
Our original coffee price is p. It doubles for 4 weeks. We can express doubling as multiplying by 2, so each week we get:
week 1 -- 2*p
week 2 -- 2*2*p
week 3 -- 2*2*2*p
week 4 -- 2*2*2*2p

We can express 2*2*2*2 as 2^4, so at the end of week 4, we have (2^4)*p.

The next week the price of the coffee triples:
week 5 -- 3*(2^4)*p

Then the price of the coffee quadruples:
week 6 -- 4*3(2^4)*p

We can multiply 4*3 to get 12, giving us 12*(2^4)*p for the price of coffee at the end of the period, which is answer choice E.
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by [email protected] » Tue Mar 13, 2018 6:57 pm
Hi lheiannie07,

We're told that the price of coffee, P, DOUBLES every week for 4 weeks, TRIPlES a week later, and finally QUADRUPLES a week after that. We're asked which of the following represents the price of coffee at the end of the period, in terms of P. This question can be solved by TESTing VALUES.

IF.... starting price = $1
Week 1 price = $2
Week 2 price = $4
Week 3 price = $8
Week 4 price = $16
Week 5 price = $48
Week 6 price = $192

So we're looking for an answer that equals 192 when P=1. There's only one answer that matches...

Final Answer: E

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by Scott@TargetTestPrep » Wed Mar 14, 2018 3:29 pm
lheiannie07 wrote:If the price of coffee, p, doubles every week for 4 weeks, triples a week later, and finally quadruples a week after that, which of the following represents the price of coffee at the end of period, in terms of p?

A. 15p
B. 7*8*p
C. 7*2^4*p
D. 3*4*8*p
E. 12*2^4*p
If the initial price of coffee is p, after week one it's 2p, after week two it's 4p, after week 3 it's 8p, and after week 4 it's 16p.

Since the price triples a week later, the new price is (3)(16p), and, since it quadruples the following week, the final price at the end of the period is (4)(3)(16p) = 12*2^4*p .

Answer: E

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