SOLUTION: Hi The school enrolment is calculated at the end of each month. Enrolment increased by 3.7% in January then decreased by 1.7% during February then increased by .80% in march.

Question 1190788: Hi
The school enrolment is calculated at the end of each month. Enrolment increased by 3.7% in January then decreased by 1.7% during February then increased by .80% in march. What was the net percentage change over the 3 months.
Thanks

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to find the growth factor, divide the percent by 100 to get the rate and than add 1 to that.

3.7% / 100 = .037 + 1 = growth factor of 1.037.
1.7% / 100 = .017 + 1 = growth factor of 1.017.
.8% / 100 = .008 + 1 = growth factor of 1.008.

if you start with 1, then:
1 * 1.037 = 1.037
1.037 * 1.017 = 1.054629
1.054629 * 1.008 = 1.063066032.

you grew from 1 to 1.063066032 in 3 cycles.
that's your overall growth rate.

to find your average growth rate per cycle, take the third root of that to get an average growth rate of 1.063066032 ^ (1/3) = 1.020594947.
if you start with 1 and multiply that by 1.020594947 ^ 3, you will get the overall growth rate of 1.063066032 as we got above.

the short hand way of finding the overall growth rate would be:
1 * 1.037 * 1.017 * 1.008 = 1.063066032.

your overall percent increase is 1.063066032 minus 1 and then * 100 to get 6.3066032%.

your average percent increase per cycle would be 1.020594947 minus 1 and then * 100 to get 2.0594947%.

let me know if you have any questions.
theo

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) increase of 3.7% --> growth factor of 1+.037 = 1.037
(2) decrease of 1.7% --> "growth" factor of 1-.017 = 0.983
(3) increase of 0.8% --> growth factor of 1+.008 = 1.008

Overall growth factor:

= 1.0275 to 4 decimal places

The percentage change over the three months is 1.0275-1 = .0275 = 2.75%.

ANSWER: 2.75%

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