6. A liquid starts at a temperature of 190 F and cools down in a room held at a constant 65 'F. Afte- minutes of cooling, it is at a temperature of 92 °F. The Fahrenheit temperature, F, can be modeled function of time in minutes, t, by the equation: F(t) = a(b) +c (a) Determine the values of the parameters a, b, and c. Round the value of b to the nearest hundredth. the equation of your final model. Show the work that leads to each of your answers. (b) Algebraically, determine the number of minutes it will take for the temperature to reach 70 °F.R the nearest tenth of a minute.

6. A liquid starts at a temperature of 190 F and cools down in a room held at a constant 65 'F. Afte- minutes of cooling, it is at a temperature of 92 °F. The Fahrenheit temperature, F, can be modeled function of time in minutes, t, by the equation: F(t) = a(b) +c (a) Determine the values of the parameters a, b, and c. Round the value of b to the nearest hundredth. the equation of your final model. Show the work that leads to each of your answers. (b) Algebraically, determine the number of minutes it will take for the temperature to reach 70 °F.R the nearest tenth of a minute.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 80 Height (metres) 40 Y 5 10 15 Time (minutes) 20 25 30

A: A graph of the trigonometric function is given, we have to find the equation of the graph.

Q: The temperature of water in a certain lake on a day in October can be determined by using the model…

Q: During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s…

A: According to the company policy we are supposed to answer only first three sub parts and rest of the…

Q: The following equation represents the relationship between hours of TV watched per day (x) and the…

A: Given dataŷ = -0.944x + 24.52x is the hours of TV watched per dayŷ is the number of situpspredicting…

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high…

A: The equation of a sinusoidal function of amplitude A, phase difference C, vertical shift D, time…

Q: Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second…

Q: The average water level in a retention pond is 6.8 ft. During a time of drought, the water level…

A: We will solve the following.

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high…

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

Q: An explosion cuses debris to rise vertically with an initial velocity of 112 feet per second. The…

A: Given that, the height of the debris above the ground is given by the function st=-16t2+112t. So,…

Question

6. A liquid starts at a temperature of 190 °F and cools down in a room held at a constant 65 F. After 10
minutes of cooling, it is at a temperature of 92 °F. The Fahrenheit temperature, F, can be modeled as
function of time in minutes, t, by the equation:
F (t)= a (b)' +c
(a) Determine the values of the parameters a, b, and c. Round the value of b to the nearest hundredth. State
the equation of your final model. Show the work that leads to each of your answers.
(b) Algebraically, determine the number of minutes it will take for the temperature to reach 70 °F. Round to
the nearest tenth of a minute.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 30 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = – 4.9t + 325t + 346. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round to the nearest tenth.) The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? (Round to the nearest tenth.) The rocket peaks at meters above sea-level.
The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…
The height of a hot air balloon can be modeled by the function S(t) = −2t2 + 60t + 1, where S(t) isthe height of the balloon, in metres, at time t minutes. a. Determine the average velocity of the hot air balloon during the first 5 minutes. b. Determine the velocity of the hot air balloon at 5 minutes.
Use the following model for the annual revenue for Amazon: R(t) = 386.06(1.31)t t is the time in years since 2020 and R(t) is in billion dollars. a) Identify whether the function is linear or exponential. Briefly explain how you know based on the formula for R(t). b) Identify the constant percent rate. Explain in a sentence what this means about Amazon's revenue changing with respect to time. c) Calculate R(0) and explain what it means in terms of Amazon's revenue and time.
Determine �→×�→, a vector perpendicular to both of the given vectors. Use the result in part (a) to determine the scalar equation of the plane that is formed by vectors �→ and �→ and goes through the origin. SEE IMAGE
NASA launches a rocket at t = O seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = – 4.9t2 + 205t + 101. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.
The national catch of Atlantic Cod has been declining in the past few decades.We can model this decline with the equationy =-0.003t2 + 0.120t + 1.909 where t is the number of years since 1950 and y is the catch in millions of metric tons.a. In which year did the catch reach its maximum?b. In which year will the catch reach 0?