2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. 50 f(t) = t2 - 20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral S”. f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).)

2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. 50 f(t) = t2 - 20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral S”. f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

See similar textbooks

Similar questions

(a) To obtain the graph of g(x)=2x1 , we start with the graph of f(x)=2x and shift it _____________ (upward/ downward) 1 unit. (b) To obtain the graph of h(x)=2x1 , we start with the graph of f(x)=2xand shift it to the (left/right) 1unit.
Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
What is the composition of two functions, fg ?
The height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?
In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?
Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.
How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?
The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. Find a reasonable domain and range for the function P.
The graph of f(x)=3x is reflected about the y-axisand stretched verticallyby a factor of 4. What isthe equation of the new function, g(x) ? State itsy-intercept, domain, and range.
Suppose you have a job that pays $8.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable x, that gives the amount of money, y, you will earn for working x hours in one week. b. Use the function rule you have written in part (a) to complete Table 4. c. Construct a line graph from the information in Table 4. d. State the domain and range of this function.