3/2/202 Sophia ::
1 Welcome
Sophia College Algebra Milestone 5.
Score 19/22
You passed this Milestone
19 questions were answered correctly.
31
UquNestiIonTs we5re a—nswerMed inIcLorrEectSly.TONE 5
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
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,3/2/202 Sophia ::
1 297 people Welcome
https://snhu.sophia.org/spcc/college-algebra-3/ 2/28
milestone_take_feedbacks/8101034
,3/2/202 Sophia ::
1 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 x. We will need to
for
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/ 3/28
milestone_take_feedbacks/8101034
, 3/2/202 Sophia ::
1 first by plugging in for the variable
Welcome
x in the function .
https://snhu.sophia.org/spcc/college-algebra-3/ 4/28
milestone_take_feedbacks/8101034
1 Welcome
Sophia College Algebra Milestone 5.
Score 19/22
You passed this Milestone
19 questions were answered correctly.
31
UquNestiIonTs we5re a—nswerMed inIcLorrEectSly.TONE 5
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
https://snhu.sophia.org/spcc/college-algebra-3/ 1/28
milestone_take_feedbacks/8101034
,3/2/202 Sophia ::
1 297 people Welcome
https://snhu.sophia.org/spcc/college-algebra-3/ 2/28
milestone_take_feedbacks/8101034
,3/2/202 Sophia ::
1 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 x. We will need to
for
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/ 3/28
milestone_take_feedbacks/8101034
, 3/2/202 Sophia ::
1 first by plugging in for the variable
Welcome
x in the function .
https://snhu.sophia.org/spcc/college-algebra-3/ 4/28
milestone_take_feedbacks/8101034
