Answer:
Step-by-step explanation:
Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have
Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising
<em>P(0) = 0 and P(50) = 1,500,000
</em>
We have and ordinary differential equation of first order that we can write
The <em>integrating factor </em>is
Multiplying both sides of the equation by the integrating factor
Hence
Integrating both sides
But P(0) = 0, so C = -3,000,000
and P(50) = 1,500,000
so
And the equation that models the number of people (in millions) who become aware of the product by time t is
Answer:
3
Step-by-step explanation:
(32-20)÷4
solve perentisis first
(12)÷4
now divide
=3
Answer:
option A is the correct answer
<span>1)The table below represents a linear function f(x) and the equation represents a function g(x):
x y
-1 -11
0 -1
1 9
g(x) = 5x + 1
Part A: Write a sentence to compare the slope of the two functions and
show the steps you used to determine the slope of f(x) and g(x). (6
points)
slope of the data of the table:
slope = rise / run = Δy / Δx = [ 9 - ( - 1) ] / [1 - 0] = 10/1 = 10
Also Δy / Δx = [-1 - (-11) ] / [ 0 - (-1) ] = 10 / 1 = 10
the slope of the function given in the form f(x) = mx + b is m, so the slope of g(x) = 5x - 1 is 5.
Comparisson: the slope of the function g(x) = 5x - 1 is half the slope of the function f(x) represented by the table.
Part B: Which function has a greater y-intercept? Justify your answer.
The y-intercept is the value of y when x = 0, so it is - 1 for the function represented by the table.
The y-intercept of a function given in the form f(x) = mx + b is b, so the y-intercept of g(x) = 5x - 1 is - 1.
So, both functions have equal y-intercept.
2)The table below shows the values of y for each value of x:
x y
1 0
1 -1
2 1
2 -2
Part A: Does the table represent a relation that is a
function? Justify your answer by using the values shown in the table. (4
points)
No, it is not a function, because the relation is ambiguous: the x-coordinate 1 may have two differente values, and the x-coordinate 2 may have two different. So you cannot determine the images of x = 1 and x = 2.
Part B: The function f(x) shown below represents the number of baskets
Jess made at different distances, x, in meters, from the hoop:
f(x) = -x + 6
Calculate and interpret the meaning of f(4). (4 points)
f(4) = - 4 + 6 = 2
It means that Jess made 2 baskets at the distant of 4 meters.
Part C: Write an ordered pair to represent the input and output of the
function in Part B when Jess is at a distance of p meters from the hoop.
(2 points)
input, p output, f(p)
6 -6 + 6 = 0
So the ordered pair is (6,0)
</span>
The first one is D. Y=-3+8x
The second one is G. -3/2x=y+2
