Question

H(t) = 88 - 37(0.85)' A human child grows rapidly in the first 36 months after birth. The given function models h, the child's height in centimeters, t months after birth for 036. Between 36 to 72 months after birth, the child grows at an average rate of 0.5 centimeter per month. Approximately how many more centimeters does the child grow in their first 36 months after birth compared to their second 36 months (36 to 72 months) after birth? Choose 1 answer: B 19 37 51 88

​

Answer 1

To compare the growth in the first and second 36-month periods, calculate the child's height at 36 months using the given growth function and subtract the constant growth during the second period. The result will show the additional growth during the first period compared to the second.

Step-by-step explanation:

To determine how many more centimeters a child grows in their first 36 months after birth compared to their second 36 months, we have to calculate the height at the end of each period and then find the difference between them. The function h(t) = 88 - 37(0.85)^t models the child's height growth during the first 36 months. For the second period, the child grows at a constant rate of 0.5 cm per month.

First, find the height at 36 months using the given function:

h(36) = 88 - 37(0.85)^36

Next, calculate the total growth during the second period (36 to 72 months):

0.5 cm/month * 36 months = 18 cm

Now, we find the height difference:

h(36) - 88 cm = total growth during the first 36 months

Subtract the growth during the second period from the total growth in the first period:

Total growth during the first 36 months - 18 cm = Additional growth during the first 36 months compared to second 36 months

Use a calculator to find the value of h(36) and perform the subtraction to get the answer.

Answer 2

Therefore, the correct option is A.

To find the correct option, we need to calculate the difference in growth between the first 36 months and the second 36 months.

1. For the first 36 months, we use the given exponential decay function
`\( h(t) = 88 - 37(0.85)^t \).`

- We find
`\( h(0) \) and \( h(36) \)` to determine the total growth in the first 36 months.

2. For the second 36 months (from 36 to 72 months), the child grows at a linear rate of 0.5 centimeters per month.

- The total growth in this period is
`\( 0.5 * 36 \)`.

3. The difference in growth is then calculated by subtracting the growth in the second period from the growth in the first period.

Given the previous calculation steps and results, we found that the child grew approximately 18.89 centimeters more in their first 36 months compared to their second 36 months.

Looking at the options provided:

A. 19

B. 37

C. 51

D. 88

The option that is closest to our calculated difference of approximately 18.89 centimeters is:

A. 19

Therefore, the correct option is A. 19.