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 number of barrels of oil a certain company exports annually increases at a rate that is proportional at any time to the number of barrels they export at that time. The company exported 5.4 million barrels annually initially, and it exported 10.8 million barrels annually after 6 years. How many million barrels of oil did the company export annually after 10 years? Round to the nearest integer. million barrels

The number of barrels of oil a certain company exports annually increases at a rate that is proportional at any time to the number of barrels they export at that time.\newlineThe company exported 55.44 million barrels annually initially, and it exported 1010.88 million barrels annually after 66 years.\newlineHow many million barrels of oil did the company export annually after 1010 years?\newlineRound to the nearest integer.\newline□\square million barrels

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Exponential growth and decay: word problemsright chevron icon

Full solution

Q. The number of barrels of oil a certain company exports annually increases at a rate that is proportional at any time to the number of barrels they export at that time.\newlineThe company exported 55.44 million barrels annually initially, and it exported 1010.88 million barrels annually after 66 years.\newlineHow many million barrels of oil did the company export annually after 1010 years?\newlineRound to the nearest integer.\newline□\square million barrels
  1. Identify growth type: Identify the type of growth. The problem states that the growth rate is proportional to the number of barrels exported at any time, which indicates exponential growth.
  2. Find initial value and factor: Determine the initial value aa and the growth factor bb. The initial value is the amount of oil exported initially, which is 5.45.4 million barrels. To find the growth factor, we need to use the information that after 66 years, the export amount doubled to 10.810.8 million barrels.
  3. Use exponential growth formula: Use the exponential growth formula to find the growth factor.\newlineThe exponential growth formula is P(t)=a⋅b(t/T)P(t) = a \cdot b^{(t/T)}, where P(t)P(t) is the amount after time tt, aa is the initial amount, bb is the growth factor, and TT is the time it takes for the initial amount to grow by the factor bb.\newlineWe know that P(6)=10.8P(6) = 10.8 and a=5.4a = 5.4, so we can set up the equation 10.8=5.4⋅b(6/T)10.8 = 5.4 \cdot b^{(6/T)}.
  4. Solve for growth factor: Solve for bb.\newlineDivide both sides by 5.45.4 to isolate b(6/T)b^{(6/T)} on one side:\newline10.85.4=b(6/T)\frac{10.8}{5.4} = b^{(6/T)}\newline2=b(6/T)2 = b^{(6/T)}\newlineSince the time it takes to double is 66 years, T=6T = 6.\newlineTherefore, b(6/6)=b1=2b^{(6/6)} = b^1 = 2.\newlineThis means the growth factor bb is 22.
  5. Find amount after 1010 years: Use the growth factor to find the amount after 1010 years.\newlineNow that we have the growth factor, we can use the formula P(t)=a⋅b(t/T)P(t) = a \cdot b^{(t/T)} to find the amount after 1010 years.\newlineP(10)=5.4⋅2(10/6)P(10) = 5.4 \cdot 2^{(10/6)}
  6. Calculate the exponent: Calculate the exponent. \newline106\frac{10}{6} simplifies to 53\frac{5}{3}, so we need to calculate 2532^{\frac{5}{3}}.\newline2532^{\frac{5}{3}} is the cube root of 252^5, which is the cube root of 3232.
  7. Calculate final amount: Calculate the final amount.\newlineP(10)=5.4×253P(10) = 5.4 \times 2^{\frac{5}{3}}\newlineP(10)=5.4×cube root of 32P(10) = 5.4 \times \text{cube root of } 32\newlineP(10)≈5.4×3.1748P(10) \approx 5.4 \times 3.1748\newlineP(10)≈17.144P(10) \approx 17.144
  8. Round to nearest integer: Round to the nearest integer.\newlineThe company exported approximately 1717 million barrels of oil annually after 1010 years.

More problems from Exponential growth and decay: word problems

Question
Use the following function rule to find f(2) f(2) .\newlinef(x)=11⋅(9)x+8 f(x) = 11 \cdot (9)^x + 8 \newlinef(2)= f(2) = _____
Get tutor helpright-arrow

Posted 5 months ago

Question
Raymond works for a pharmaceutical company that is testing the effectiveness of a new medication. He gave one of the study participants 400400 milligrams of the medication, and he knows the amount remaining in the participant's body will decrease by a factor of 1/31/3 each hour.\newlineWrite an exponential equation in the form y=a(b)xy = a(b)^x that can model the amount of medication, yy, remaining in the participant's body after xx hours.\newlineUse whole numbers, decimals, or simplified fractions for the values of aa and bb.\newliney=y = ______\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
A colony of 100100 bacteria doubles in size every 6060 hours. What will the population be 180180 hours from now??
Get tutor helpright-arrow

Posted 4 months ago

Question
Charlotte opened a savings account and deposited $800.00\$800.00 as principal. The account earns 8%8\% interest, compounded annually. What is the balance after 1010 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.
Get tutor helpright-arrow

Posted 4 months ago

Question
Bob rented a car for a flat fee of `$150` and an additional `$10` per day. Write a linear function that represents the total cost, f(x)f(x), after xx days.
Get tutor helpright-arrow

Posted 10 months ago

Question
Sally purchased a laptop for `$800` and has to pay a service fee of `$20` for each day until it is delivered. Write a linear function to represent the total cost, h(x)h(x), after xx days.
Get tutor helpright-arrow

Posted 10 months ago

Question
Kevin invested $1,000\$1,000 in a savings account with a daily interest rate of 0.1%0.1\%. Write an exponential function to represent the total amount, s(x)s(x), in his account after xx days.
Get tutor helpright-arrow

Posted 9 months ago

Question
A=2450+740s A=2450+740 s \newlineThe total amount, A A , in thousands of dollars, of scholarship money given out by a college throughout its history at a time of s s semesters after the summer of the year 20002000 is given by the equation. What was the total amount of scholarship money, in thousands of dollars, given out by the college up to the summer of the year 20002000 ?
Get tutor helpright-arrow

Posted 5 months ago

Question
T=235+980d T=235+980 d \newlineThe torque, T T , in newton-meters, on a diving board with a 100100 kilogram weight placed d d meters from the diving board's fulcrum is given by the equation. How much torque in newton-meters is on the diving board when the weight is placed at the fulcrum?
Get tutor helpright-arrow

Posted 8 months ago

Question
R=42−0.7t R=42-0.7 t \newlineQuinn returned home one summer's day to find it extremely hot. He turned the air conditioner on, and the room's temperature began decreasing at a constant rate. The given equation shown gives the room's temperature, R R , in degrees Celsius, t t minutes after Quinn turned on the air conditioner. What was the room's temperature, in degrees Celsius, when Quinn returned home?
Get tutor helpright-arrow

Posted 7 months ago

View all (161)

Related topics

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