If f(x) is an exponential function where f(3) = 18 and f(7.5) = 60, then find the
value of f(12), to the nearest hundredth.

If F(x) Is An Exponential Function Where F(3) = 18 And F(7.5) = 60, Then Find Thevalue Of F(12), To The

Answers

Answer 1

Given:

f(x) is an exponential function where f(3) = 18 and f(7.5) = 60.

To find:

The value of f(12), to the nearest hundredth.

Solution:

Let the exponential function be

[tex]f(x)=ab^x[/tex]         ...(i)

It is given that [tex]f(3) = 18[/tex]. Substitute [tex]x=3[/tex] in (i).

[tex]f(3)=ab^3[/tex]

[tex]18=ab^3[/tex]           ...(ii)

It is given that [tex]f(7.5) = 60[/tex]. Substitute [tex]x=7.5[/tex] in (i).

[tex]f(7.5)=ab^{7.5}[/tex]

[tex]60=ab^{7.5}[/tex]           ...(iii)

Divide (iii) by (ii).

[tex]\dfrac{60}{18}=\dfrac{ab^{7.5}}{ab^3}[/tex]

[tex]\dfrac{10}{3}=b^{4.5}[/tex]

[tex]\left(\dfrac{10}{3}\right)^\frac{1}{4.5}=b[/tex]

[tex]b\approx 1.30676[/tex]

Putting [tex]b=1.30676[/tex] in (ii), we get

[tex]18=a(1.30676)^3[/tex]

[tex]\dfrac{18}{(1.30676)^3}=a[/tex]

[tex]a\approx 8.0665[/tex]

Putting [tex]a=8.0665[/tex] and [tex]b=1.30676[/tex] in (i), we get

[tex]f(x)=8.0665(1.30676)^x[/tex]

Putting x=12, we get

[tex]f(12)=8.0665(1.30676)^{12}[/tex]

[tex]f(12)=200.0024[/tex]

[tex]f(12)\approx 200.00[/tex]

Therefore, the value of f(12) is about 200.00.


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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

4.5 cm

Step-by-step explanation:

Given that the end points of PG are given. Find the length of segment PQ using the Pythagorean theorom p(-4.3) and q(0,5)

Solution

Using the formula;

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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y-x=x-y/2
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Answers

Answer:

1 Simplify 75\times 875×8 to 600600.

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Answer:

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Explanation:

4(6+2.4)/2.4 = 14

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Answers

Answer:

Step-by-step explanation:

2A:3B

= 5:6

3B:2C

= 36:15

A:C

= ?:?

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answer:

-4x-10

Step-by-step explanation:

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Answers

Answer:

[tex]y^2-\frac{7}{2}y+3[/tex]

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

9514 1404 393

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

I am sorry but it is just an example !


Question ) A university has 30,330 students. In a random sample of 270 students, 18 speak three or more languages. Predict the number of students at the university who speak three or more languages.

Answer ) 2,022 students will speak three or more languages

Here's why:
Using proportions.
18. x
--- =. ----
270. 30,330

Cross multiply
18 x 30,330 = 545,940
270 multiply x = 270x
545,940 divided by 270 = 2,022
x = 2,022 students

please help_________​

Answers

Answer:

[tex]11\sqrt{797}\pi[/tex]

Step-by-step explanation:

[tex]A=\pi r \sqrt{h^2+r^2}[/tex]

the radius is 22/2 = 11 in

h is 26 in

substitute: [tex]\pi \left(11\right)\sqrt{\left(26^2\right)+\left(11^2\right)}[/tex]

= [tex]11\sqrt{797}\pi[/tex]

Answer:

286π in²

Step-by-step explanation:

The lateral area (A) of the cone is calculated as

A = πrs ( r is the radius and s the slant height )

Here r = 22 ÷ 2 = 11 and s = 26 , then

A = π × 11 × 26 = 286π in²

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Answers

Answer:

10ft

Step-by-step explanation:

volume= 502 ft³

or, πr²h= 502ft³

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Answers

Iam not very sure but i think y=22.5

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Answers

Answer:

5 miles

Step-by-step explanation:

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