1/5 times 8 =? help please asap

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

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

As

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

So

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

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

$y=27000$

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

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6 0

3 years ago

How might the crisis in biodiversity lead to a food crisis for humans?

EleoNora [17]

Answer:

Hi and heres your answer!

Step-by-step explanation:

The crisis of biodiversity will lead to a food crisis for humans because:

1.No varieties in certain foods like plants and animals that are healthy

2.The Less food there is,more animals go extinct which means humans will go extinct too.

and finally 3: Without certain types of species like the bee, humans have no chance of survival (since bees pollinate flowers,fruits,and plants which could be used for human consumption and medicine)

Hope this helped

Plz mark brainliest

Dont forget smash that heart at the bottom <3

Have a great day,Youre amazing!

7 0

2 years ago

Kendra has a painting canvas that is 20 inches wide by 37 inches high. She painted a red rose, which covered 50% of the canvas.

uysha [10]

The total area is:
A = (20) * (37)
A = 740 in ^ 2
We can make the following rule of three:
740in ^ 2 -----> 100%
x --------------> 50%
Clearing x we have:
x = (50/100) * (740)
x = 370 in ^ 2
Answer:
the area of the canvas which was covered by the red rose was:
x = 370 in ^ 2

6 0

3 years ago

What is the greastest common factor of 56 and 84

Assoli18 [71]

The factors of 56: 1; 2; 4; 7; 8; 14; 28; 56
The factors of 84: 1; 2; 3; 4; 6; 14; 28; 42; 84

GCF(56; 84) = 28

4 0

3 years ago

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Which step comes first? 12÷3•(15-6)+3

bagirrra123 [75]

Pemdas

Parentheses
Exponents
Multiply
Divide
Add
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3 0

3 years ago

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