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ZanzabumX [31]
3 years ago
12

Given the function h(x) = 4^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Mathematics
2 answers:
Gennadij [26K]3 years ago
4 0
Ooh, fun

the average rate of change is the slope

easy, so for section A, it would be the slope from (0,h(0)) to (1,h(1)) or from (0,1) to (1,4)
slope=(y2-y1)/(x2-x1)=(4-1)/(1-0)=3/1=3


section B, would be slope from (2,h(2)) to (3,h(3)) or from
(2,16) to (3,64)
slope=(y2-y1)/(x2-x1)=(64-16)/(3-2)=48/1=48


1. section A has an average rate of change of 3
section B has an average rate of change of 48



2. 48 is how many times greater than 3
48/3=16
16 times greater

it is because it is an exponential function and the slope grows bigger
Tems11 [23]3 years ago
3 0
Heyo Ace Baby!

First of all, a rate of change can be expressed as a slope. A <span>slope is the ratio of the vertical and horizontal changes between two points. Average rate is always equal for every point and the line is straight.

So, our function is h(x) = </span>4^x

we substitute the values and remember, x = 0 is the rise and x =1 is the run, our changes applies to x and h(x)

h(x) = 4^0 = 1 and 4^1 = 4

So, with the formula (y2-y1)/x2-x1) you can find the average rate (and let's say that you can find it also with (changes of h(x)) / (changes of x)). h(x) is considered as "y"

Section A = \frac{4-1}{1-0} =  \frac{3}{1} = 3

Let's work out the Section B...4^2 = 16 and 4^3 = 64

Section B = \frac{64-16}{3-2} =  \frac{48}{1} = 48

Let's find how bigge ris 48 than 3

48 : 3 = 16

16 times, because our function is exponential and slope is bigger in section B
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1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.

2)The solution for b² - 4b + 4 = 0 is x=2.

<u>Step-by-step explanation</u>:

The general form of quadratic equation is ax²+bx+c = 0

where

  • a is the coefficient of x².
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1) The given quadratic equation is m² - 5m - 14 = 0.

From the above equation, it can be determined that b = -5 and c = -14

The roots are -7 and 2.

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The solution is given by (x-2) (x-2) = 0.

Therefore, the solution is x=2.

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