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ella [17]
1 year ago
8

If f(x)f(x) is an exponential function where f(3.5)=12f(3.5)=12 and f(9)=75f(9)=75, then find the value of f(7.5)f(7.5), to the

nearest hundredth.
Mathematics
1 answer:
nignag [31]1 year ago
6 0

Using an exponential function, it is found that f(7.5) = 45.5.

<h3>What is an exponential function?</h3>

An exponential function is modeled by:

y = ab^x.

In which:

  • a is the initial value.
  • b is the rate of change.

For this problem, we have that f(3.5) = 12, then:

y = ab^x

12 = ab^{3.5}

a = \frac{12}{b^{3.5}}

We also have that f(9) = 75, then:

y = ab^x

75 = ab^9

Since a = \frac{12}{b^{3.5}}:

75 = \frac{12}{b^{3.5}} \times b^9

b^{5.5} = \frac{75}{12}

\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}

b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}

b = 1.39542165

Then:

75 = ab^9

a = \frac{75}{1.39542165^9}

a = 3.7386

Hence:

y = 3.7386(1.39542165)^x

When x = 7.5, we have that:

y = 3.7386(1.39542165)^{7.5} = 45.5

Hence f(7.5) = 45.5.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

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with Judy jogging north and Jackie jogging west (on straight roads). When Jackie is 1 mile farther fro m the intersection than J
miskamm [114]
Let the distance of Judy from intersection is x and distance of Jackie from intersection is y.

We convert the given information to equations, step by step.

Point 1: When Jackie is 1 mile farther from the intersection than Judy.

This means y is 1 mile more than x.

So,

y = 1 + x

Point 2: The distance between them is 2 miles more than Judy’s distance from the intersection. 

Distance between is x+ y.

So, x+y is 2 miles more than y.

x+y = y + 2
⇒
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From point 1 we have:

y = 1 + x = 1+ 2 = 3

So,

Distance of Judy from intersection is 2 miles and distance of Jackie from intersection is 3 miles.
4 0
2 years ago
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Dennis_Churaev [7]

9514 1404 393

Answer:

  the lines are perpendicular

Step-by-step explanation:

You can tell something by looking at the differences of coordinates:

  B-A = (6-2, -11-5) = (4, -16) . . . . . Δy/Δx = -16/4 = -4

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The product of the slopes of these lines is (-4)(1/4) = -1, so ...

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4 0
2 years ago
Find the measure of each bolded arc. Round to the nearest hundredth
vladimir1956 [14]

Answer:

Arc Length = 68.7

Step-by-step explanation:

The formula that is used to find the arc length:

s = (θ/360) * 2πr

(You would get the value of θ, by subtracting 57 from 360)

(You would get r by dividing 26 by 2)

Now we can solve this;

s = (303/360) 2π(13)

s = 0.842 * 2π(13)

s = 0.842 * 0.283(13)

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Hope this helps!

5 0
3 years ago
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground need
dalvyx [7]

Answer:

Length = 20.49 yards and Width = 12.49 yards.

Step-by-step explanation:

The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:

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x^2 + 8x = 256. Applying the completing the square method gives:

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(x+4)^2 = 272. Taking square root on both sides gives:

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x = 12.49 or x = -20.49.

Since length cannot be negative, therefore x = 12.49 yards.

Since smaller side = x yards, thus smaller side = 12.49 yards.

Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.

Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!

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10 m-1n-5 , for m = 10 and n= -2
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Answer:

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