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h(t)=88-37(0.85)^(t) 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 0 <= t <= 36. 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: (A) 19 (B) 37 (C) 51 (D) 88

h(t)=88−37(0.85)t h(t)=88-37(0.85)^{t} \newlineA human child grows rapidly in the first 3636 months after birth. The given function models h h , the child's height in centimeters, t t months after birth for 0≤t≤36 0 \leq t \leq 36 . Between 3636 to 7272 months after birth, the child grows at an average rate of 00.55 centimeter per month. Approximately how many more centimeters does the child grow in their first 3636 months after birth compared to their second 3636 months ( 3636 to 7272 months) after birth?\newlineChoose 11 answer:\newline(A) 1919\newline(B) 3737\newline(C) 5151\newline(D) 8888

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Q. h(t)=88−37(0.85)t h(t)=88-37(0.85)^{t} \newlineA human child grows rapidly in the first 3636 months after birth. The given function models h h , the child's height in centimeters, t t months after birth for 0≤t≤36 0 \leq t \leq 36 . Between 3636 to 7272 months after birth, the child grows at an average rate of 00.55 centimeter per month. Approximately how many more centimeters does the child grow in their first 3636 months after birth compared to their second 3636 months ( 3636 to 7272 months) after birth?\newlineChoose 11 answer:\newline(A) 1919\newline(B) 3737\newline(C) 5151\newline(D) 8888
  1. Calculate Child's Height: First, we need to calculate the child's height at 3636 months using the given function h(t)=88−37(0.85)th(t) = 88 - 37(0.85)^t. Let's plug in t=36t = 36 into the function. h(36)=88−37(0.85)36h(36) = 88 - 37(0.85)^{36}
  2. Calculate 0.85360.85^{36}: Now, we need to calculate the value of 0.850.85 raised to the power of 3636. \newline(0.85)36≈0.049(0.85)^{36} \approx 0.049
  3. Find Height at 3636 Months: Substitute the value back into the function to find the height at 3636 months.\newlineh(36)=88−37×0.049h(36) = 88 - 37 \times 0.049\newlineh(36)≈88−1.813h(36) \approx 88 - 1.813\newlineh(36)≈86.187h(36) \approx 86.187 cm
  4. Calculate Growth 3636−72-72 Months: Next, we calculate the total growth in height from 3636 to 7272 months. Since the child grows at an average rate of 0.5 cm/month0.5 \, \text{cm/month} for these 3636 months, we multiply the rate by the number of months.\newlineGrowth from 3636 to 7272 months = 0.5 cm/month×36 months0.5 \, \text{cm/month} \times 36 \, \text{months}\newlineGrowth from 3636 to 7272 months = 18 cm18 \, \text{cm}
  5. Find Growth 00−36-36 Months: Now, we need to find the difference in growth between the first 3636 months and the second 3636 months. We know the child's height at birth is 0 cm0\,\text{cm} and at 3636 months is approximately 86.187 cm86.187\,\text{cm}. \newlineGrowth in the first 3636 months = h(36)−h(0)h(36) - h(0)\newlineGrowth in the first 3636 months = 86.187 cm−0 cm86.187\,\text{cm} - 0\,\text{cm}\newlineGrowth in the first 3636 months = 86.187 cm86.187\,\text{cm}
  6. Find Difference in Growth: Finally, we subtract the growth in the second 3636 months from the growth in the first 3636 months to find the difference.\newlineDifference in growth = Growth in the first 3636 months - Growth in the second 3636 months\newlineDifference in growth = 86.18786.187 cm - 1818 cm\newlineDifference in growth ≈68.187\approx 68.187 cm

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