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:

A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was 64 . The number increased by 50 percent each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by 50 percent per year. What is the difference in the number of chickens between these two situations two years from now? Choose 1 answer: (A) 0 (B) 189 (C) 405 (D) 11

A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was 6464. The number increased by 50%50\% each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by 50%50\% per year. What is the difference in the number of chickens between these two situations two years from now?\newlineChoose 11 answer:\newline(A) 00\newline(B) 189189\newline(C) 405405\newline(D) 1111

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Understanding integersright chevron icon

Full solution

Q. A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was 6464. The number increased by 50%50\% each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by 50%50\% per year. What is the difference in the number of chickens between these two situations two years from now?\newlineChoose 11 answer:\newline(A) 00\newline(B) 189189\newline(C) 405405\newline(D) 1111
  1. Calculate Chickens After 44 Years: First, let's calculate the number of chickens at the end of the four-year period with a 50%50\% increase each year.\newlineInitial number of chickens: 6464\newlineYearly increase: 50%50\%\newlineWe will use the formula for compound interest to calculate the number of chickens after four years, which is similar to calculating the future value of an investment.\newlineNumber of chickens after nn years = Initial number ×(1+rate)n\times (1 + \text{rate})^n
  2. Calculate Chickens After 22 Years: Now, let's calculate the number of chickens after four years.\newlineNumber of chickens after 44 years =64×(1+0.50)4= 64 \times (1 + 0.50)^4\newline=64×(1.50)4= 64 \times (1.50)^4\newline=64×5.0625= 64 \times 5.0625\newline=324= 324 (rounded to the nearest whole number)
  3. Constant Increase Calculation: Next, we need to calculate the number of chickens two years from now under the first scenario where the number of chickens increases at a constant rate equal to the rate of the most recent year.\newlineThe rate of the most recent year is 50%50\% of the number of chickens at the end of the fourth year.\newlineConstant increase = 50%50\% of 324324\newline= 0.50×3240.50 \times 324\newline= 162162\newlineSo, the number of chickens will increase by 162162 each year for the next two years.
  4. Calculate Chickens After 22 More Years: Now, let's calculate the number of chickens after two more years with the constant increase.\newlineNumber of chickens after 22 more years (constant increase) = 324+162×2324 + 162 \times 2\newline= 324+324324 + 324\newline= 648648
  5. 5050% Increase Calculation: For the second scenario, we need to calculate the number of chickens two years from now if the number continues to increase by 5050 percent per year.\newlineNumber of chickens after 11 more year (5050% increase) = 324×(1+0.50)324 \times (1 + 0.50)\newline= 324×1.50324 \times 1.50\newline= 486486\newlineNumber of chickens after 22 more years (5050% increase) = 486×(1+0.50)486 \times (1 + 0.50)\newline= 486×1.50486 \times 1.50\newline= 729729
  6. Calculate Difference: Finally, we calculate the difference in the number of chickens between the two scenarios two years from now.\newlineDifference = Number of chickens after 22 more years (5050% increase) - Number of chickens after 22 more years (constant increase)\newlineDifference = 729−648729 - 648\newlineDifference = 8181

More problems from Understanding integers

Question
Function g g can be thought of as a scaled version of f(x)=∣x∣ f(x)=|x| .\newlineWhat is the equation for g(x) g(x) ?\newlineChoose 11 answer:\newline(A) g(x)=−43∣x∣ g(x)=-\frac{4}{3}|x| \newline(B) g(x)=43∣x∣ g(x)=\frac{4}{3}|x| \newline(C) g(x)=−34∣x∣ g(x)=-\frac{3}{4}|x| \newline(D) g(x)=34∣x∣ g(x)=\frac{3}{4}|x|
Get tutor helpright-arrow

Posted 8 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 53 \frac{5}{3} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=−53∣x∣ y=-\frac{5}{3}|x| \newline(B) y=35∣x∣ y=\frac{3}{5}|x| \newline(C) y=−∣x−5∣+3 y=-|x-5|+3 \newline(D) y=∣x−3∣+5 y=|x-3|+5
Get tutor helpright-arrow

Posted 10 months ago

Question
Aiden has $200 \$ 200 with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get 4040 hats. If Aiden purchases only t t -shirts, he will get 80 80 t\mathrm{t} -shirts. Which of the following best models the relationship between the number of hats, h h , and the number of t \mathrm{t} -shirts, t t , that Aiden could purchase with this money?\newlineChoose 11 answer:\newline(A) 40h+80t=400 40 h+80 t=400 \newline(B) 80h+40t=200 80 h+40 t=200 \newline(C) 5h+2.5t=200 5 h+2.5 t=200 \newline(D) 2.5h+5t=200 2.5 h+5 t=200
Get tutor helpright-arrow

Posted 10 months ago

Question
We want to find the intersection points of the graphs given by the following system of equations:\newline{x−y=−4y=5(x+1)2−3 \left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right. \newlineOne of the intersection points is (−2,2) (-2,2) .\newlineFind the other intersection point. Your answer must be exact.
Get tutor helpright-arrow

Posted 10 months ago

Question
Derrick has 22 \mathbf{2 2} dollars. Colleen has x x dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?\newlineChoose 11 answer:\newline(A) x−22 x-22 \newline(B) x+22 x+22 \newline(C) 22x 22 x \newline(D) 22x+22 22 x+22
Get tutor helpright-arrow

Posted 10 months ago

Question
Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 3030 meters and a depth of 1515 meters. He wants to increase the radius to 4040 meters and the depth to 2020 meters. How much more water will the pond hold, in thousands of cubic meters?\newline(Round to the nearest thousand cubic meters.)
Get tutor helpright-arrow

Posted 4 months ago

Question
Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are 3636 inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?\newlineChoose 11 answer:\newline(A) 3232 inches\newline(B) 4242 inches\newline(C) 5555 inches\newline(D) 6060 inches
Get tutor helpright-arrow

Posted 7 months ago

Question
Ari thinks the perfect milkshake has 55 scoops of ice cream for every 33 spoonfuls of caramel. Freeze Zone makes batches of milkshakes with 1010 scoops of ice cream and 77 spoonfuls of caramel.\newlineWhat will Ari think about the amount of caramel in Freeze Zone's milkshakes?\newlineChoose 11 answer:\newline(A) Freeze Zone's milkshakes have too much caramel.\newline(B) Freeze Zone's milkshakes have too little caramel.\newline(C) Freeze Zone's milkshakes are just right.
Get tutor helpright-arrow

Posted 8 months ago

Question
Nayeli lights a 4 m2 4 \mathrm{~m}^{2} space with 1212 candles. Citlali lights a 10 m2 10 \mathrm{~m}^{2} space with 3030 of the same type of candles.\newlineWhose space is lit brighter?\newlineChoose 11 answer:\newline(A) Nayeli's area\newline(B) Citlali's area\newline(C) The spaces are equally bright.
Get tutor helpright-arrow

Posted 5 months ago

Question
Lashawn makes scrambled eggs with 33 spoonfuls of salsa for every 22 eggs. Gilberta adds 77 spoonfuls of salsa for every 55 eggs.\newlineWhose scrambled eggs have a stronger salsa taste?\newlineChoose 11 answer:\newline(A) Lashawn's eggs\newline(B) Gilberta's eggs\newline(C) The dishes of scrambled eggs have equal salsa tastes.
Get tutor helpright-arrow

Posted 8 months ago

View all (19)

Related topics

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