23.

Question

A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5000 wasps, the situation can be modeled by which equation?

(1 point)
Responses

w(t) = 5000(13)t
where w(t) is the number of wasps after t months
w(t) = 5000(13)t
where w(t) is the number of wasps after t months

w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months

w(t) = 5000(87)t
where w(t) is the number of wasps after t months
w(t) = 5000(87)t
where w(t) is the number of wasps after t months

w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
w(t) = 50(1.13)t
where w(t) is the number of wasps after t months
Question 2
24.

Which of the following statements is true about the above wasp equation?

(1 point)
Responses

As t increases, w increases slowly at first and then quickly
As t increases, w increases slowly at first and then quickly

As t increases, w increases quickly at first and then slowly
As t increases, w increases quickly at first and then slowly

As t increases, w decreases slowly at first and then quickly
As t increases, w decreases slowly at first and then quickly

As t increases, w decreases quickly at first and then slowly
As t increases, w decreases quickly at first and then slowly
Question 3
25.

Given the explicit formula for the sequence in function notation, find the 5th term of the sequence.

f(n) = 2n−1

(1 point)
f(5) =

Question 4
26.

Use the explicit formula An=4.8 + (n − 1)2
to find the 11th term in the described arithmetic sequence.

(1 point)
A11 =

Question 5
27.

Manuel has saved $253.32 so far. He plans to put $50 into his savings each month for the next year. How much money will Manuel have after a year of savings?

(1 point)
$

Question 6
28.

Use the table to answer the question.



The sequences for the two functions is shown in the table. Which of the following statements are true?

(1 point)
Responses

While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).
While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).

None of the above
None of the above

The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.
The growth rate of g(x) is initially greater than the growth rate of f(x) between the second and the fifth term.

While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
While the growth rate of g(x) is initially greater that the growth rate of f(x), the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x).
Question 7
29..

Consider the sequence 41, 29, 17, 5...

The recursive function is ________ with A1 =
____.

(1 point)
Responses

An= An−1+12, 53
An= An−1+12, 53

An= An−1−12, 41
An= An−1−12, 41

An= 12An−1, −12
An= 12An−1, −12
Question 8
30.

Which function represents exponential decay?

(1 point)
Responses

y = .8 (3)x
y = .8 (3)x

y = 3 (4 )x
y = 3 (4 )x

y = 3(.5)x
y = 3(.5)x

y = 2(1.5)x
y = 2(1.5)x
Skip to navigation

Answer 1

Let's answer each of your questions one by one.

Question 1: Exponential Growth Equation

The growth of the wasp population can be modeled by the equation: w(t) = 5000(1.13)^t where w(t) is the number of wasps after t months. Thus, the correct answer is:

• w(t) = 5000(1.13)^t where w(t) is the number of wasps after t months

Question 2: Growth Behavior

The statement that is true about the wasp equation is:

• As t increases, w increases slowly at first and then quickly.

Question 3: 5th Term of the Sequence

To find the 5th term using the formula f(n) = 2n - 1:

• f(5) = 2(5) - 1 = 10 - 1 = 9. Thus, f(5) = 9.

Question 4: 11th Term of the Arithmetic Sequence

To find the 11th term using the formula A(n) = 4.8 + (n - 1)2:

• A(11) = 4.8 + (11 - 1) × 2 = 4.8 + 10 × 2 = 4.8 + 20 = 24.8. Thus, A(11) = 24.8.

Question 5: Manuel's Savings After a Year

Manuel has saved $253.32 and plans to put $50 into his savings each month for 12 months:

• Total savings after one year = $253.32 + (50 × 12) = $253.32 + $600 = $853.32. Thus, Manuel will have $853.32 after a year of savings.

Question 6: Growth Rates of Two Functions

Without seeing the actual growth rates in the table, a general statement that could often be true in such scenarios would be:

• While the growth rate of f(x) is initially greater than the growth rate of g(x), the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x). However, confirm by comparing the sequences.

Question 7: Recursive Function

For the sequence 41, 29, 17, 5, we can see that each term decreases by 12:

• The recursive function is An = An−1 − 12, A1 = 41.

Question 8: Function Representing Exponential Decay

The function that represents exponential decay has a base between 0 and 1:

• y = 3(0.5)^x represents exponential decay.

If you need further clarifications or assistance, feel free to ask!