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:

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time. The town consumed 4.4 trillion British thermal units (BTUs) initially, and it consumed 5.5 trillion BTUs annually after 5 years. What is the town's annual energy consumption, in trillions of BTUs, after 9 years? Choose 1 answer: (A) 6.6 (B) 32.8 (C) 41.8

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.\newlineThe town consumed 44.44 trillion British thermal units (BTUs) initially, and it consumed 55.55 trillion BTUs annually after 55 years.\newlineWhat is the town's annual energy consumption, in trillions of BTUs, after 99 years?\newlineChoose 11 answer:\newline(A) 66.66\newline(B) 3232.88\newline(C) 4141.88

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Estimate population size using proportionsright chevron icon

Full solution

Q. The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.\newlineThe town consumed 44.44 trillion British thermal units (BTUs) initially, and it consumed 55.55 trillion BTUs annually after 55 years.\newlineWhat is the town's annual energy consumption, in trillions of BTUs, after 99 years?\newlineChoose 11 answer:\newline(A) 66.66\newline(B) 3232.88\newline(C) 4141.88
  1. Identify Initial and Final Amounts: Identify the initial and final amounts of energy consumption and the time it took to reach the final amount from the initial amount.\newlineInitial energy consumption: 4.44.4 trillion BTUs\newlineEnergy consumption after 55 years: 5.55.5 trillion BTUs\newlineTime taken to reach 5.55.5 trillion BTUs from 4.44.4 trillion BTUs: 55 years
  2. Calculate Rate of Increase: Calculate the rate of increase per year using the proportional relationship.\newlineLet the rate of increase be represented by ' extit{k}' (a constant).\newlineUsing the formula for exponential growth: Final amount = Initial amount ×e(k×time)\times e^{(k \times \text{time})}\newline5.5=4.4×e(k×5)5.5 = 4.4 \times e^{(k \times 5)}
  3. Solve for Rate Constant: Solve for the rate constant kk.5.54.4=ek×5\frac{5.5}{4.4} = e^{k \times 5}1.25=ek×51.25 = e^{k \times 5}Take the natural logarithm (ln) of both sides to solve for kk.ln⁡(1.25)=ln⁡(ek×5)\ln(1.25) = \ln(e^{k \times 5})ln⁡(1.25)=k×5\ln(1.25) = k \times 5k=ln⁡(1.25)5k = \frac{\ln(1.25)}{5}
  4. Calculate Value of 'k': Calculate the value of 'k'.\newlinek=ln⁡(1.25)5k = \frac{\ln(1.25)}{5}\newlinek≈0.0455k \approx \frac{0.045}{5}\newlinek≈0.009k \approx 0.009
  5. Use 'k' to Find Consumption: Use the rate constant 'k' to find the energy consumption after 99 years.\newlineEnergy consumption after 99 years = Initial amount ×e(k×time)\times e^{(k \times \text{time})}\newlineEnergy consumption after 99 years = 4.4×e(0.009×9)4.4 \times e^{(0.009 \times 9)}
  6. Calculate Consumption After 99 Years: Calculate the energy consumption after 99 years.\newlineEnergy consumption after 99 years = 4.4×e(0.009×9)4.4 \times e^{(0.009 \times 9)}\newlineEnergy consumption after 99 years ≈4.4×e0.081\approx 4.4 \times e^{0.081}\newlineEnergy consumption after 99 years ≈4.4×1.08447\approx 4.4 \times 1.08447\newlineEnergy consumption after 99 years ≈4.77167\approx 4.77167 trillion BTUs
  7. Round Final Answer: Round the final answer to one decimal place as the options are given in one decimal place.\newlineEnergy consumption after 99 years ≈4.8\approx 4.8 trillion BTUs

More problems from Estimate population size using proportions

Question
Bob's Gift Shop sold 250250 cards for Mother's Day. One salesman, Arturo, sold 10% 10 \% of the cards sold for Mother's Day. How many cards did Arturo sell?\newlineAnswer:
Get tutor helpright-arrow

Posted 8 months ago

Question
Valeria drew a scale drawing of a farm. The goat pen, which is 20 meters20\,\text{meters} long in real life, is 5 millimeters5\,\text{millimeters} long in the drawing. What is the scale of the drawing?\newline1 millimeter:_____ meters1\,\text{millimeter} : \_\_\_\_\_\,\text{meters}
Get tutor helpright-arrow

Posted 8 months ago

Question
Naira paddled with the current in the same amount of time as it took her to paddle against the current. Naira paddled at an average rate of xx relative to the water each way. Assume the speed of the current was constant. What was the speed of the current? Naira paddled with the current in the same amount of time as it took her to paddle against the current. Naira paddled at an average rate of xx relative to the water each way. Assume the speed of the current was constant. What was the speed of the current? Naira paddled with the current in the same amount of time as it took her to paddle against the current. Naira paddled at an average rate of xx relative to the water each way. Assume the speed of the current was constant. What was the speed of the current? Naira paddled with the current in the same amount of time as it took her to paddle against the current. Naira paddled at an average rate of xx relative to the water each way. Assume the speed of the current was constant. What was the speed of the current? Naira paddled with the current in the same amount of time as it took her to paddle against the current. Naira paddled at an average rate of xx relative to the water each way. Assume the speed of the current was constant. What was the speed of the current?
Get tutor helpright-arrow

Posted 5 months ago

Question
The area in thousands of square kilometers of 1919 countries in East and Southeast Asia are shown in the dot plot. Each value is rounded to the nearest 250250 thousand square kilometers. China, which has an area of 99,597597 thousand square kilometers, was excluded from the data. If China were included, then which of the following changes would NOT occur?
Get tutor helpright-arrow

Posted 5 months ago

Question
the number of muskrats in a 144144 acre area is estimated to be 27362736. What is the estimated population density\newlineA) 1919 muskrats per acre\newlineB) 2020 muskrats per acre\newlineC) 2121 muskrats per acre\newlineD) 2222 muskrats per acre
Get tutor helpright-arrow

Posted 4 months ago

Question
Maya's school is having a spring carnival. When Maya carries a bin of water balloons outside for the balloon toss, she trips and breaks 1111 balloons. She counts the remaining water balloons, and there are 1313 left. Which equation can you use to find the number of water balloons ww in the bin before Maya trips?
Get tutor helpright-arrow

Posted 3 months ago

Question
In a telephone poll of 2828 people, 88 people said they like shopping. What is the ratio of the number of people who like shopping to the total number of people polled? Write your answer as two numbers separated by a colon (for example, 2:32:3).
Get tutor helpright-arrow

Posted 3 months ago

Question
Alderwoman Natalia polled a random sample of residents in her district about new affordable housing projects in the district. The results of the poll are most representative of which of the following populations?\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

Question
Jeanne's bank account earns interest annually. The equation shows her starting balance of $500\$500 and her balance at the end of three years, $546.36\$546.36. At what rate rr did Jeanne earn interest?\newline546.36=500(1+r)546.36 = 500(1 + r)
Get tutor helpright-arrow

Posted 1 month ago

View all (5)

Related topics

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