Answer:
a)
b) 6.84 million
c) 2028.52
d) 47 years
Step-by-step explanation:
a)Here we know standard exponential growth rate is
In this put t=0 and a(t)=6.27 million
thus we get a = 6.27 million
now
this is equal to(in 2012)=
b)Put t = 6
we get
=6.84 million
c)
take log both sides
we get 16.52 years
d)
take log both sides we get 47 years to get double the current population.
<u>Part A</u>
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So, the x-intercepts are
<u>Part B</u>
The vertex will be a minimum because the coefficient of is positive.
The x-coordinate of the vertex is
Substituting this back into the function, we get
So, the coordinates of the vertex are
<u>Part C</u>
Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.
The graph is shown in the attached image.
<u>Note: this answer assumes the equation of the line can be put in slope-intercept form. </u>
Answer:
Step-by-step explanation:
1) First, find the slope of y + 7 = -2 (x - 6). We can see that it's already in point-slope form, or format. Remember that the number in place of the
is the slope. Therefore, -2 is the slope of that equation.
What we need is the slope that is perpendicular to that, though. So, find the opposite reciprocal of -2. To do this, change its sign, convert it into a fraction (), and flip its numerators and denominators. Therefore, the perpendicular slope would be
.
2) Now that we have a slope and a point the line passes through, we can write an equation using the point-slope formula, . In order to write an equation, the
,
, and
have to be substitute for with real values.
The represents the slope. We already calculated that in the last step, so put
in place of the
. The
and
represent the x and y values of a point the line passes through. We know that the line has to pass through (6, -3), so substitute 6 for
and -3 for
:
Therefore, (again, assuming that the line can be put in point-slope form) the answer is .