a) Increasing function.
b) The growth factor is 4.
c) The asymptote is y tending to zero as x tends to negative infinity.
d) y = 1
c) The graph can be seen at the end.
<h3>
What conclusions can we get about the given function?</h3>
Here we are given the following exponential function:
y =f(x) = 4^x
a) First, we want to know if the function is increasing or decreasing. Remember that a function is increasing if, as x increses, also does the value of y.
Here clearly we have an increasing function.
- f(0) = 4^0 = 1
- f(1) = 4^1 = 4
- f(2) = 4^2 = 16
and so on...
b) Now we want to identify the growth factor. This is the number that is being exponentiated, so in:
y = 4^x
The growth factor is 4.
c) We have an asymptote as x tends to negative infinity, because we will eventually have denominator that tends to infinity, then we will have an asymptote that tends to zero, as x tends to negative infinity.
d) The y-intercept is what we get when we evaluate in x = 0, we have:
y = f(0) = 4^0 = 1
The y-intercept is y = 1.
e) The sketch of the exponential function can be seen in the image below.
If you want to learn more about exponential functions:
brainly.com/question/11464095
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Answer:
21.99 units
164.93 units²
Step-by-step explanation:
given radius r = 15 units
angle of sector = 84°
Length of sector =
x 2 x π x r
=
x 2 x 3.14 x 15
= 21.99 units
Area of sector =
x π x r²
=
x 3.14 x 15²
= 164.93 units²
Answer:
100 minutes
Step-by-step explanation:
First lets find out total how many time they spent on those activities
He spent in driving: 3*60 + 1/4*60=195 minutes
He spent in gardening: 1*60 + 3/4*60=95 minutes
In this way by subtracting from minutes spent during driving to minutes spent during gardening we can know he spent 100 minutes longer
The required expression is 100 - 0.2w
Step-by-step explanation:
Given,
Amount of radioactive substance = 100 mg
The substance decreases by 20% each week.
To find the remaining amount of the in w weeks.
Now,
Each week 20% = 0.2 of the substance will be decreased.
So, in w weeks 0.2×w of the the substance will be decreased.
Hence,
The remaining substance = 100 - 0.2w