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3 years ago

What is the average rate of change for the function f(x)=3(0.25)^x over the interval -2 ≤ x ≤ 0

1 answer:

8 0

Answer:
-22.5

Explanation:
Use the average rate of change equation
f(b)-f(a) / b-a
f(b) = f(0) = 3(.25)^0 = 3
f(a) = f(-2) = 3(.25)^-2 = 48

(3-48)/ 0-(-2)
(-45) / 2
-22.5

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What is 153/4 as a whole number

maw [93]

$\frac{4}{3} = \frac{51}{n} \\ = > \frac{3}{4} = \frac{n}{51 } \\ = > n = \frac{3}{4} \times 51 \\ = > n = \frac{153}{4} \\ = > n = 38 \frac{1}{4}$

Hope you could get an idea from here.

Doubt clarification - use comment section.

6 0

2 years ago

Find the average value of the function on the given interval.<br> f(x)=2 ln x; [1,e]

JulijaS [17]

Answer:

$f_{avg}=\frac{1}{e-1}$

Step-by-step explanation:

We are given that a function

$f(x)=2lnx$

We have to find the average value of function on the given interval [1,e]

Average value of function on interval [a,b] is given by

$\frac{1}{b-a}\int_{a}^{b}f(x)dx$

Using the formula

$f_{avg}=\frac{1}{e-1}\int_{1}^{e}lnx dx$

By Parts integration formula

$\int(uv)dx=u\int vdx-\int(\frac{du}{dx}\int vdx)dx$

u=ln x and v=dx

Apply by parts integration

$f_{avg}=\frac{1}{e-1}([xlnx]^{e}_{1}-\int_{1}^{e}(\frac{1}{x}\times xdx))$

$f_{avg}=\frac{1}{e-1}(elne-ln1-[x]^{e}_{1})$

$f_{avg}=\frac{1}{e-1}(e-0-e+1)=\frac{1}{e-1}$

By using property lne=1,ln 1=0

$f_{avg}=\frac{1}{e-1}$

8 0

3 years ago

A store sells packages of comic books with a poster. A poster and 5 comics cost $15.75 A poster and 11 comics cost $27.75 Writ

Vanyuwa [196]

Answer:

y=x+5.99

Step-by-step explanation:

A poster and 2 comics cost $7.99

(2,7.99)

A poster and 11 comics cost $16.99.

(11,16.99)

Let y be the cost of package and x be the no. of comics

We will use two point slope form :

(x1,y1) = (2,7.99)

(x2,y2) = (11,16.99)

Formula :

y-y1 = y2-y1/x2-x1(x-x1)

Substitute the values:

Hence a linear function rule that models the cost y of a package containing any number x of comic books is y=x+5.99

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3 years ago

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algol [13]

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3 years ago

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lukranit [14]

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3 years ago