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KonstantinChe [14]
4 years ago
15

A community college enrolled 96,000 students in 2007, and the enrollment has increased by 7% every year since then. Graph the ex

ponential function, y, that gives the number of students enrolled in terms of t, where t is the number of years since 2007.
-The graph of the function begins at y = 96,000.
-The graph of the function does not have any asymptotes.
-The graph of the function shows the exponential growth.
-As t increases in the exponential function, the value of y approaches zero.
Mathematics
1 answer:
PtichkaEL [24]4 years ago
5 0
The formula of the function would be:
y = 96000(1.07)^t

The graph is an exponential function with y-intercept of 9600. The curve goes upward indefinitely as the value of time increases.

Therefore, from the choices, the statements that apply to the graph are:
-The graph of the function begins at y = 96,000.
-The graph of the function shows the exponential growth.
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-3/5 is a whole number
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2^x=40 (Round to the nearest hundredth.)
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Which of the fractions are equivalent to 6/8 ? Select all that apply.
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abcdef

Step-by-step explanation:

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3 years ago
3) Cory is standing on a cliff that is 48 feet above the ground. He throws a rock in to the air. The height, h, of the rock
Nadusha1986 [10]

Answer:

a) The initial height of the rock is of 48 feet.

b) It takes 1 seconds for the rock to reach maximum height.

c) The rock's maximum height is 50 feet.

d) It takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

f(x) = ax^{2} + bx + c

It's vertex is the point (x_{v}, f(x_{v})

In which

x_{v} = -\frac{b}{2a}

If a<0, the vertex is a maximum point, that is, the maximum value happens at x_{v}, and it's value is f(x_{v})

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

The height of the ball after t seconds, in feet, is given by:

h(t) = -2t^2 + 4t + 48

Which is a quadratic equation with a = -2, b = 4, c = 48

a) What is the initial height?

This is h(0) = 48. So the initial height of the rock is of 48 feet.

b) How many seconds does it take to reach the maximum height?

This is the value of t at the vertex. So

t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1

It takes 1 seconds for the rock to reach maximum height.

c) What is the rock's maximum height?

This is the height of the ball after 1 second. So

h(1) = -2(1)^2 + 4(1) + 48 = 50

The rock's maximum height is 50 feet.

d) How many seconds does it take to for the rock to land on the ground?

This is t for which h(t) = 0, so we solve the quadratic equation.

\bigtriangleup = (4)^2-4(-2)(48) = 400

t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4

t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6

Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.

5 0
3 years ago
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