



 
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,  


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