1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?

Question

14-03-2018
Mathematics

contestada

1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?

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CastleRook CastleRook · Answer 1 · 2018-03-23T11:13:17+01:00

1. f(x)=8/1+3e^(-0.7x)
to get f(-3) we substitute the value and solve the equation as follows:
f(-3)=8/1+3e^(-0.7*3)
f(-3)=8.36737
which can also be written as:
f(-3)-8.36737=0

2. f(x)=20/1+9e^(3x)
to get the y-intercept we let x=0, hence we shall have:
f(0)=20/1+9e^(3*0)
f(0)=20+9*1
f(0)=20+9
f(0)=29
the y-intercept is at point (0,29)

3. f(x)=24/1+3e^(-1.3x)
Given that the expression above has no denominator, then the domain of the expression is all real numbers then the expression has not vertical asymptote.The same applies for horizontal asymptote and the oblique.

4. f(x)=15/1+4e^(-0.2x)
The graph is not increasing at any point, this means that it does not have a point of maximum growth.

5. f(x)=24/1+3e^(-1.3x)
The graph of the function is a decay graph, this means that there is no point in which the graph is increasing hence there's not growth rate.