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Question 1

23.

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

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).

None of the above
None of the above

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).
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
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1 answer

Here are the answers to the questions provided:

Question 1 & 2

Question 1: The situation can be modeled by the equation:

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

Question 2: The correct statement about the growth of wasps is:

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

Question 3

Given the explicit formula f(n) = 2n − 1, find the 5th term:

  • f(5) = 2(5) − 1 = 10 − 1 = 9

Question 4

Using the formula \( A_n = 4.8 + (n - 1)2 \) to find the 11th term:

  • A(11) = 4.8 + (11 - 1)2 = 4.8 + 20 = 24.8

Question 5

To find the total amount of money Manuel will have after a year:

  • Monthly saving = $50
  • Total saving in one year (12 months) = 50 * 12 = $600
  • Total amount after a year = $253.32 + $600 = $853.32

Question 6

To determine the truth about the growth rates of the sequences:

  • The statement:
  • While the growth rate of g(x) is initially greater than 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

For the sequence 41, 29, 17, 5…:

  • The recursive function can be expressed as:
  • An = An−1 - 12, A1 = 41

Question 8

Identifying the function that represents exponential decay:

  • y = 3(0.5)^x

These answers should provide you with clarity on the concepts discussed in your questions!