<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
The growth factor between 
and 
is given by:
![\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]](https://tex.z-dn.net/?f=%5Cleft%5B3%5Cleft%285%5Cright%29%5E3%5Cright%5D%5Cdiv%20%5Cleft%5B3%5Cleft%285%5Cright%29%5E1%5Cright%5D)
![\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375](https://tex.z-dn.net/?f=%5Cmathrm%7BCalculate%5C%3Awithin%5C%3Aparentheses%7D%5C%3A%5Cleft%5B3%5Cleft%285%5Cright%29%5E3%5Cright%5D%5C%3A%3A%5Cquad%20375)
![\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15](https://tex.z-dn.net/?f=%5Cmathrm%7BCalculate%5C%3Awithin%5C%3Aparentheses%7D%5C%3A%5Cleft%5B3%5Cleft%285%5Cright%29%5E1%5Cright%5D%5C%3A%3A%5Cquad%2015)
So,
= 
= 
Similarly, growth factor between 
and 
is given by:
![\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]](https://tex.z-dn.net/?f=%5Cleft%5B3%5Cleft%285%5Cright%29%5E7%5Cright%5D%5Cdiv%20%5Cleft%5B3%5Cleft%285%5Cright%29%5E5%5Cright%5D)
= 
= 
= 
= 
=
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 
is an exponential function.
The graph for 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
where
= Initial population amount
= growth rate
= time
Substituting the values in the function
So, the population be in 24 years
As
So
Therefore, the population be in 24 years will be 27000.
Also, the population growth modeled by an exponential function as 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 
when it is replaced by f(x- 3/5).
We already have an idea that rule for horizontal translation:
- Given a function
, and a constant c > 0, the function 
represents a horizontal shift c units to the right from f(x). The function 
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
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