00:02
For this problem, we are told that according to the yenz model for predicting the height of preschool children, the rate of growth of a typical preschool child is given by the formula below, and we are told that the height of a typical three -month -old preschool child is 60 .30 centimeters.
00:18
For part a, we are asked, what is the height of a typical infant at age t? so we can find the height by finding the anti -derivative of the equation above.
00:29
So, the first term will, the t for the first term, will go to t to the power of 5 over 5, which means that that will turn out as 0 .2098, t to the power of 5.
00:42
Then the second term would go to t to the power of 4 over 4 with the constant in front, so it would go to minus 0 .0638, t to the power of 4.
00:54
Third term will go to t to power of 3 over 3 with the constant in front.
00:59
So that will be reduced down to plus 4 .253 t cubed.
01:07
Then the t term here is going to go to t squared over 2 with the coefficient in front.
01:12
So that's going to become minus 12 .856 t squared...