Rates of change, linear approximations, etc.

[goldenthread]

Anyone want to walk me through these?

On a particular snowy day, the depth of snow on the ground is modeled by S(t) = 0.512t - 0.422sin(t-3.580), where S(t) is measured in inches and t is measured in hours.

(a) Find the average rate of change of S(t) over the interval 0 <= t <= 24. Indicate units of measure in the problem.

(b) Find the value of S'(15). Using correct units, interpret the meaning of the value in the context of the problem.

(c) Find the time t for which the rate at which snow is accumulating is equal to the average rate of change over the interval [0,24].

(d) For t>24, L(t), the linear approximation to S at t=24, is a better model for the amount of snow on the ground. Use L(t) to predict the time at which there will be 18 inches of snow on the ground. Show the work that leads to your answer.

 

[HallsofIvy]

Anyone want to walk me through these?

On a particular snowy day, the depth of snow on the ground is modeled by S(t) = 0.512t - 0.422sin(t-3.580), where S(t) is measured in inches and t is measured in hours.

(a) Find the average rate of change of S(t) over the interval 0 <= t <= 24. Indicate units of measure in the problem.

(b) Find the value of S'(15). Using correct units, interpret the meaning of the value in the context of the problem.

(c) Find the time t for which the rate at which snow is accumulating is equal to the average rate of change over the interval [0,24].

(d) For t>24, L(t), the linear approximation to S at t=24, is a better model for the amount of snow on the ground. Use L(t) to predict the time at which there will be 18 inches of snow on the ground. Show the work that leads to your answer.

Where did you get this problem? It looks like a pretty typical Calculus problem but you seem to being saying that you are not taking nor have taken a Calculus course.

(a) asks you to find the "average" of a continuous function, between t= b and t= a, is \(\displaystyle \frac{\int_a^b f(t) dt}{b- a}\). Can you do that integral?

(b) asks you to find the derivative of a sine function. Do you not how to do that?

(c) asks you to determine the value of t when your answer to (a) is equal to you answer to (b).

(d) The "linear approximation to function f(t) at t= a" is y= f'(a)(t- a)+ f(a).

 

[stapel]

Anyone want to walk me through these?

Sure! Please reply showing how far you've gotten, clearly stating where you're getting confused, and we can try to help you get going again. Thank you!