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3 years ago

M=-2 b=(0,4) find the equation of the line with the given slope and intercept

Mathematics

1 answer:

Korvikt [17]3 years ago

4 0

Answer:

y = -2x +4

Step-by-step explanation:

The equation of a line is written as y = mx+b. Since m= -2 and b = 4, the the equation is y = -2x + 4.

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

$3^{\frac{1}{8}\cdot \:24}=3^3$

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

#learnwithBrainly

6 0

3 years ago

A fish tank is 60% if the way full when it has 25 gallons. How many total gallons can the fish tank hold ?

sdas [7]

The tank can hold 31.8 gallons of water.

3 0

3 years ago

Liz and Alana each participate in the home that jump at the track meet Liz’s high jump was 1 meter Alana’s high jump was 132 cen

brilliants [131]

1 meter is 100 centimeters, therefore Alana jumped higher by 32 centimeters.
132-100=32

7 0

3 years ago

What dose this equal 2(6x-4)=3(6x+2)

AveGali [126]

Answer:

-7/3

Step-by-step explanation:

2(6−4)=3(6+2)

2(6x-4)=3(6x+2)

Solve

Distribute

2(6−4)=3(6+2)

{\color{#c92786}{2(6x-4)}}=3(6x+2)

12−8=3(6+2)

{\color{#c92786}{12x-8}}=3(6x+2)

Distribute

12−8=3(6+2)

12x-8={\color{#c92786}{3(6x+2)}}

12−8=18+6

12x-8={\color{#c92786}{18x+6}}

Add

to both sides of the equation

12−8=18+6

12x-8=18x+6

12−8+8=18+6+8

12x-8+{\color{#c92786}{8}}=18x+6+{\color{#c92786}{8}}

5 more steps

Solution

=−7/3

7 0

2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20-%2011%20%3D%207%20-%20x" id="TexFormula1" title=" - 11 = 7 - x" alt=" - 11 = 7 - x" align=

Oksana_A [137]

X = 18
if you need the steps i could give them to you just ask!
Hope that helped!
:)

5 0

3 years ago