Finding the Specific Position FunctionI was driving to a birthday party at my friend's housewhen I had the realization: I forgot the birthday gift. Myvelocity at t seconds after the realization is measuredin meters per second and given by the functionv(t) = 20 – 21, where traveling towards my friend'sLabelEquation/ValueGeneral AntiderivativeVt) = 201 – P + CDisplacement on [0,10]100house is the positive direction.Displacement on [10,20]-100As we've seen in class, a function does not have aunique antiderivative; in our example here, you couldplug ANY number you want in for C, and we would getthat V(t) =v(t). So, we don't have enoughOh no! The gift!Friend's Houseinformation to find the exact position function. Buteverything changes as soon as we are given somepoint on our position function.Suppose that I was 2.4 kilometers (note the units!)away from home when I made the realization. What iss(0) ? (Recall that we use s(t) to represent theMy houseposition function.)s(0) =%3D-10101520-10Graph of my velocity at time t

Answered: Image /qna-images/answer/17e40a34-1ae5-469b-b4bc-a4489be17d6b.jpg

Answered: Suppose that I was 2.4 kilometers (note…

Suppose that I was 2.4 kilometers (note the units!) away from home when I made the realization. What is s(0) ? (Recall that we use s(t) to represent the position function.) s(0) =

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Finding the Specific Position Function
I was driving to a birthday party at my friend's house
when I had the realization: I forgot the birthday gift. My
velocity at t seconds after the realization is measured
in meters per second and given by the function
v(t) = 20 – 21, where traveling towards my friend's
Label
Equation/Value
General Antiderivative
Vt) = 201 – P + C
Displacement on [0,10]
100
house is the positive direction.
Displacement on [10,20]
-100
As we've seen in class, a function does not have a
unique antiderivative; in our example here, you could
plug ANY number you want in for C, and we would get
that V(t) =v(t). So, we don't have enough
Oh no! The gift!
Friend's House
information to find the exact position function. But
everything changes as soon as we are given some
point on our position function.
Suppose that I was 2.4 kilometers (note the units!)
away from home when I made the realization. What is
s(0) ? (Recall that we use s(t) to represent the
My house
position function.)
s(0) =
%3D
-10
10
15
20
-10
Graph of my velocity at time t

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.