Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

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

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 5 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 6 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 7 months ago

View all (427)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant