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:

Fred started studying how the number of branches on his tree grows over time. The relationship between the elapsed time t, in years, since Fred started studying the tree, and the number of its branches, B_("year ")(t), is modeled by the following function: B_("year ")(t)=20*(2.5)^(t) Complete the following sentence about the monthly rate of change in the number of branches. Round your answer to two decimal places. Every month, the number of branches increases by a factor of

Fred started studying how the number of branches on his tree grows over time.\newlineThe relationship between the elapsed time t t , in years, since Fred started studying the tree, and the number of its branches, Byear (t) B_{\text {year }}(t) , is modeled by the following function:\newlineByear (t)=20⋅(2.5)t B_{\text {year }}(t)=20 \cdot(2.5)^{t} \newlineComplete the following sentence about the monthly rate of change in the number of branches.\newlineRound your answer to two decimal places.\newlineEvery month, the number of branches increases by a factor of

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compound interest: word problemsright chevron icon

Full solution

Q. Fred started studying how the number of branches on his tree grows over time.\newlineThe relationship between the elapsed time t t , in years, since Fred started studying the tree, and the number of its branches, Byear (t) B_{\text {year }}(t) , is modeled by the following function:\newlineByear (t)=20⋅(2.5)t B_{\text {year }}(t)=20 \cdot(2.5)^{t} \newlineComplete the following sentence about the monthly rate of change in the number of branches.\newlineRound your answer to two decimal places.\newlineEvery month, the number of branches increases by a factor of
  1. Understand function representation: Understand the given function and what it represents.\newlineThe function Byear(t)=20×(2.5)tB_{\text{year}}(t)=20\times(2.5)^{t} represents the number of branches on the tree after tt years. To find the monthly rate of change, we need to express tt in months instead of years.
  2. Convert time to months: Convert the time from years to months.\newlineSince there are 1212 months in a year, we need to find the equivalent monthly growth factor. Let's denote mm as the number of months. Then, tt (in years) is equal to m12\frac{m}{12} (since mm months is m12\frac{m}{12} years).
  3. Rewrite function in terms of months: Rewrite the function in terms of months.\newlineThe new function in terms of mm (months) will be Bmonth(m)=20⋅(2.5)m12B_{\text{month}}(m)=20\cdot(2.5)^{\frac{m}{12}}.
  4. Calculate monthly growth factor: Calculate the monthly growth factor.\newlineWe need to find the value of (2.5)112(2.5)^{\frac{1}{12}} to determine by what factor the number of branches increases each month.
  5. Evaluate growth factor: Evaluate (2.5)1/12(2.5)^{1/12} using a calculator.\newline(2.5)1/12≈1.0912(2.5)^{1/12} \approx 1.0912 (rounded to four decimal places for intermediate calculation).
  6. Round growth factor: Round the monthly growth factor to two decimal places as instructed.\newlineThe monthly growth factor rounded to two decimal places is approximately 1.091.09.

More problems from Compound interest: 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 (3)

Related topics

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