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Illusion [34]
3 years ago
10

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

and x = 7?
A) 5
B) 25
C) 125
D) 625

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?
A) 12,000; linear
B) 18,000; exponential
C) 20,000; linear
D) 27,000; exponential


What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(x- 3/5)?
A) translate vertically 3/5 units up
B) translate vertically 3/5 units down
C) translate horizontally 3/5 units left
D) translate horizontally 3/5 units right
Mathematics
1 answer:
notsponge [240]3 years ago
6 0
<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

#learnwithBrainly

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