(1 point) The series ∑Cn(x+4)n converges at x=0 and diverges at x=−11. Based on this information we know something about how big
1 answer:
Answer:
R must lie between the two values 4 and 7
R ∈ (4,7)
Step-by-step explanation:
∑
converges at x= 0 and Diverges at x= -11
Given series is centered at x= -4
since the series converges at x= 0, which is a distance of 4 from x= -4
=> the radius of convergence (R) is at least 4
since the series diverges at x= -11, which is a distance of 7 from x= -4
=> the radius of convergence (R) cannot be more than 7
=> 4 ≤ R ≤ 9 ⇒ R ∈ (4,7)
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<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:
So,
=
=
Similarly, growth factor between and
is given by:
=
=
=
=
=
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.
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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