Sophia College Algebra Milestone 5.
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Score 19/22
You passed this Milestone
19 questions were answered correctly.
UNIT 5 — MILESTONE 5
31 questions were answered incorrectly.
Susan monitors the number of strep infections reported in a certain neighborhood in a given week. The recent
numbers are shown in this table:
Week Number of People
0 20
1 26
2 34
3 44
According to her reports, the reported infections are growing at a rate of 30%.
If the number of infections continues to grow exponentially, what will the number of infections be in week
10?
203 people
206 people
276 people
297 people
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RATIONALE
In general, exponential growth is modeled using this equation. We will use information from
the problem to find values to plug into this equation.
The initial number of infections is , so this is the value for a. The infection rate is ,
so this is our value for b (remember to write it as a decimal). We want to know how many
infections there will be in week 10, so we will use for the value for x. We will need to
solve for y. Start by simplifying what's inside the parentheses.
1 plus is . Next, take this value to the power of .
to the power of is . Finally, multiply this by .
There will be 276 people infected in week 10.
CONCEPT
Exponential Growth
2
Suppose and .
Find the value of .
RATIONALE
To evaluate this composite function, focus on the innermost function first. Evaluate
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8101034 2/28
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first by plugging in for the variable x in the function .
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8101034 3/28
,3/2/2021 Sophia :: Welcome
Score 19/22
You passed this Milestone
19 questions were answered correctly.
UNIT 5 — MILESTONE 5
31 questions were answered incorrectly.
Susan monitors the number of strep infections reported in a certain neighborhood in a given week. The recent
numbers are shown in this table:
Week Number of People
0 20
1 26
2 34
3 44
According to her reports, the reported infections are growing at a rate of 30%.
If the number of infections continues to grow exponentially, what will the number of infections be in week
10?
203 people
206 people
276 people
297 people
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8101034 1/28
,3/2/2021 Sophia :: Welcome
RATIONALE
In general, exponential growth is modeled using this equation. We will use information from
the problem to find values to plug into this equation.
The initial number of infections is , so this is the value for a. The infection rate is ,
so this is our value for b (remember to write it as a decimal). We want to know how many
infections there will be in week 10, so we will use for the value for x. We will need to
solve for y. Start by simplifying what's inside the parentheses.
1 plus is . Next, take this value to the power of .
to the power of is . Finally, multiply this by .
There will be 276 people infected in week 10.
CONCEPT
Exponential Growth
2
Suppose and .
Find the value of .
RATIONALE
To evaluate this composite function, focus on the innermost function first. Evaluate
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8101034 2/28
, 3/2/2021 Sophia :: Welcome
first by plugging in for the variable x in the function .
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8101034 3/28
