Mathematics, 14.12.2019 08:31 amanda2003teddy

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. f(x) = 5x + 4 h(x) = x2 + 8x + 24

x = -3
x = 3
x = 4
x = 5

Answers: 1

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The exponential function is $f(x)= 5^{x} +4$
The polynomial function is $h(x)= x^{2} +8x+24$

We want a value of x as such that $f(x)\ \textgreater \ h(x)$ , so

$5^{x}+4$ > $x^{2} +8x+24$

We are provided with four possible value of x. By process of trial and error, we will narrow down two values of x when the statement is changing from false to true

first, we try x=-3

by substituting into f(x)

and

$f(-3)=5^{-3}+4 = 4.008$ and $h(-3)= (-3)^{2}+8(-3)+24=9$
so f(x)

which is not the inequality wanted

We try x=3

by substituting into f(x)

and

$f(3)= 5^{3}+4=129$ and $h(3)= (3)^{2}+8(3)+24=57$ ,
so f(x)

as wanted

We know that any values of

greater than three will give f(x)

greater than h(x)

, so we narrow down to two values that make the statement changes from false to true.

There is one value between -3 and three that makes f(x)

greater than h(x)

. From here we use the method of trial and error.

We can start with the mid value between -3 and three which is 0
$f(0)= 5^{0}+4=5$
$h(0)= 0^{2}+8(0)+24=24$
f(x)

is less than h(x)

which isn't the inequality we want so here we narrow down the value of x must be between 0 and 3

We can try mid-value between 0 and three which is 1.5
$f(1.5)= 5^{1.5}+4=15.18$
$h(1.5)= (1.5)^{2}+8(1.5)+24=38.25$
f(x)

is still less than h(x)

, so we now narrow down the value of x between 1.5 and 3

We try again using the mid-value between 1.5 and three which is 2.25
$f(2.25)= 5^{2.25}+4=41.38$
$h(2.25)= 2.25^{2}+8(2.25)+24=47.0625$
We still have f(x)

less than

so we can narrow down further the value of x between 2.25 and 3 (which is quite a short interval already)

We can keep trying by choosing a value of x says x=2.6
$f(2.6)= 5^{2.6}+4=69.66$
$h(2.6)= 2.6^{2}+8(2.6)+24=51.56$
We have f(x)

greater then h(x)

The narrowing down process continues where we now have the interval of x between 2.25 and 2.6. Keeping to one decimal place we can find the
value of x=2.4 is the approximate value where f(x)

is greater than h(x)

.

x=2.4

Answer from: Quest

idek

step-by-step explanation:

Answer from: Quest

answer: 7 x 2/5 = 2.8 hours, is your answer. your welcome! : 3

step-by-step explanation: first work out how long it took to hose 1/7 of the lawn which is 2/5 hours. times that by 7 to get the whole lawn.

sorry i don't know the other answer. i didn't learn what a proportional relationship is.

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