I hope this helps you
A law firm charges a client according to the function f(x)=4(x+2) , where x represents the number of hours spent on the client’s
case each week, and f(x) represents the total charge that week in hundreds of dollars. Which graph best represents f(x)? A
image 9aa1ffbf4b6c4b819528d03e38d40220
B
image 2613910ac77a443ab121eae0681d4242
C
image 9a1a98d3a68b4a5b91b8831ed35dc6ef
D
image 85146317251e4058afc4ecb02264fffa
image 9aa1ffbf4b6c4b819528d03e38d40220
B
image 2613910ac77a443ab121eae0681d4242
C
image 9a1a98d3a68b4a5b91b8831ed35dc6ef
D
image 85146317251e4058afc4ecb02264fffa
1 answer:
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x ---> the number of hours spent on the client’s case each week
f(x) ----> the total charge that week in hundreds of dollars
we have
distribute
This is the equation of the line in slope intercept form
where
The slope or unit rate is
The y-intercept or initial value is
To graph the line we need minimum two points
Find the x-intercept
For f(x)=0
The x-intercept is the point (-2,0)
so
we have
the points (-2,0) and (0,8)
To graph the line, plot the intercepts, connect them and join the points
The graph in the attached figure
Remember that the value of x and the value of f(x) cannot be a negative number
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Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)