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rewona [7]
3 years ago
9

What is the average rate of change of the function f(x)=4(2)^x from x = 0 to x = 2? Enter your answer in the box.

Mathematics
2 answers:
bekas [8.4K]3 years ago
3 0

average rate of change is just the slope from (0,f(0)) to (2,f(2))


basically, average rate of change=slope=\frac{f(2)-f(0)}{2-0}

evalaute each

f(2)=4(2)^2=4(4)=16

f(0)=4(2)^0=4(1)=4


so average rate of change=\frac{16-4}{2-0}=\fracc{12}{2}=6

average rate of change is 6

ycow [4]3 years ago
3 0

6 Just took the test. X)

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The ratio of the sides of two similar octagons is 2:5. What is the ratio of the perimeters of these octagons?
Tom [10]
So we see the ratio of the sides of two similar octagons is 2:5 so let's say the first octagon has a side of 2 and the other has a side of 5. 2*8 = 16 and 5*8 = 40. 16:40 = 4:10 = and is again 2:5. So the answer is 2:5.
4 0
3 years ago
1.What is the equation of the line perpendicular to  that passes through ? Write your answer in slope-intercept form. Show your
Juliette [100K]

Answer:

1. Use a compass to make arc marks which intersect above and below then connect.

2. y=\frac{1}{3}x + 2

Step-by-step explanation:

1. To construct a perpendicular line, use a compass to draw arc marks from one end of the segment through point P. Then repeat this again at the other end. This means at point P there will be two intersecting arc marks. Repeat the process down below with the same radius as used above. Then connect the two intersections.

2. The point slope form of a line is (y-y_1)=m(x-x_1) where x_1=-3\\y_1=1. We write  

(y-1)=m(x--3)\\(y-1)=m(x+3)  

Since the line is to be perpendicular to the line shown it will have the negative reciprocal to the slope of the function 3x+y =-8. To find m, rearrange the function to be y=-8-3x. The slope is -3 and the negative reciprocal will be 1/3.

(y-1)=\frac{1}{3}(x+3)  

Simplify for slope intercept form.

(y-1)=\frac{1}{3}(x+3)\\(y-1)=\frac{1}{3}x+1\\y=\frac{1}{3}x + 2


3 0
3 years ago
Then determine which answer
shtirl [24]

Answer:

B.

Step-by-step explanation:

The graph that is going to show the function, has two parts: one for numbers equal or less than 3 and the other for numbers greater than 3

Then, for x≤3, the function is f(x) = 4. This is a constant so the graph is a horizontal line.

Additionally, for x>3, the function is f(x)=12x. This is a straight line with a positive slope.

So, the answer that follows these 2 conditions is B.

3 0
3 years ago
What is the x-value of the solution? -x + 2y = 6 6y= x + 18
oksano4ka [1.4K]
Our x equals 0 so the answer is 0

3 0
3 years ago
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas
Mazyrski [523]

Answer:

The population in 40 years will be 1220.

Step-by-step explanation:

The population of a town grows at a rate proportional to the population present at time t.

This means that:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The initial population of 500 increases by 25% in 10 years.

This means that P(0) = 500, P(10) = 1.25*500 = 625

We apply this to the equation and find t.

P(t) = P(0)e^{rt}

625 = 500e^{10r}

e^{10r} = \frac{625}{500}

e^{10r} = 1.25

Applying ln to both sides

\ln{e^{10r}} = \ln{1.25}

10r = \ln{1.25}

r = \frac{\ln{1.25}}{10}

r = 0.0223

So

P(t) = 500e^{0.0223t}

What will be the population in 40 years

This is P(40).

P(t) = 500e^{0.0223t}

P(40) = 500e^{0.0223*40} = 1220

The population in 40 years will be 1220.

7 0
3 years ago
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