At the end of the first day, 7 weeds appear in your neighborhood park. Each day, the number of weeds increases by four times. How many weeds will be in the park at the end of 14 days?

Question

stacey · Answer

day 1:  7  weeds
day 2:  7 * 4  weeds
day 3:  (7*4) * 4 = 7 * 4^2
day 4:  (7 * 4^2) * 4 = 7 * 4^3
Notice that since we keep multiplying by 4, the exponent on 4 keeps increasing so that on day n, there are [7 * 4^(n-1)]  weeds.

anonymous · Answer

i tried to find the answer but couldnt cuz i dont got a calculaotr so can you answer it please?

stacey · Answer

469,762,048

stacey · Answer

If you type 7*4^13 into google, it will also act as a calculator for you.

anonymous · Answer

626,349,395 
   392 
   71 
   35,456,231 
 choices ^^^^^^^^

gw2011 · Answer

Stacey's answer is correct.  Here is the formula for calculating this problem:

(7)(4)^(n-1)  where n is the year you are looking for

(7)(4)^(14-1)=(7)(4)^13=469,762,048

gw2011 · Answer

Sorry, I wrote incorrectly that n is the year you are looking for, it should n is the day you are looking for.

stacey · Answer

Okay. So that means that the problem means for the increase to be 4 times the increase of the previous day.
day 1:  7  weeds   (increase is 7)
day 2:  7 + (7 * 4)  weeds   (increase is 7 * 4)
day 3:  7 + (7 * 4) + (7 * 4^2) weeds
day 4:  7 + (7 * 4) + (7 * 4^2) + (7 * 4^3)   weeds
That means we are looking for the sum of a geometric sequence.
$$s _{n}=[a*(r ^{n}-1)] / (r-1)$$
where a is the first term, r is the ratio (what we multiply by, and n is the number of terms (days).

stacey · Answer

$$s_{n}=[7∗(4^{14}−1)]/(4−1)$$

anonymous · Answer

thats not the right answer it has to be one of the choices

stacey · Answer

If you put 7*(4^14-1)/(4-1) into google, it will calculate it and you will get one of your choices.