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raketka [301]
2 years ago
15

The graph of an exponential function has a y-intercept of 7 and contains the point (4,112). Construct the exponential function T

hat describes the graph.
Mathematics
1 answer:
blondinia [14]2 years ago
3 0

The exponential function that describes the graph is y=7\cdot 2^x

The standard form of an exponential function is expressed as y=ab^x

a is the y-intercept

(x, y) is the point on the graph

Given the following expression

a = 7

(x, y) = (4, 112)

Substitute the given values into the exponential equation

y = ab^x\\112=7\cdot b^4\\b^4 = \frac{112}{7}\\b^4= 16\\b =\sqrt[4]{16}\\b = 2

Get the required exponential equation

Recall that y=ab^x, hence the required equation will be y=7\cdot 2^x

Learn more here: brainly.com/question/19245707

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Suppose an airline policy states that all baggage must be box shaped with a sum of​ length, width, and height not exceeding 114
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Answer:

Step-by-step explanation:

Represent the length of one side of the base be s and the height by h.  Then the volume of the box is V = s^2*h; this is to be maximized.

The constraints are as follows:  2s + h = 114 in.  Solving for h, we get 114 - 2s = h.

Substituting 114 - 2s for h in the volume formula, we obtain:

V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)

This is to be maximized.  To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:

dV

----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2

ds

Simplifying this, we get dV/ds = -4s^2 + 114s = 0.  Then either s = 28.5 or s = 0.

Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in

and the volume is V = s^2(h) = 46,298.25 in^3

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3 years ago
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