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 Question from Pauline, a student: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth

Hi Pauline,

Suppose the child's height at birth is $a$ units. The child's height increases 5% per month and at the beginning of the second month her height is $a + 0.05a = 1.05a$ units. At the beginning of the third month her height has increased by 5% of her height at the beginning of the second month so her height is $1.05a + 0.05 (1.05a) = 1.05a( 1.05) = (1.05)^2 a$ units.

What is her height at the beginning of the fourth month? What is her height at the beginning of the $n^{th}$ month?

I hope this helps,
Penny

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