You passed this Milestone
19 questions were answered correctly.
3 questions were answered incorrectly.
1
Susan monitors the number of strep infections reported in a certain neighborhood in a given week. The recent
n
...
You passed this Milestone
19 questions were answered correctly.
3 questions were answered incorrectly.
1
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 . The infection rate is ,
so this is our value for (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 . We will need to
solve for . Start by simplifying what's inside the parentheses.
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
first by plugging in for the variable in the function .
a
b
x
y
1
x
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Once has been replaced with , evaluate the expression.
The function evaluates to . To evaluate , use the value of , which is
, as the input for the function .
Once has been replaced with , evaluate the expression.
This tells us that is equal to .
CONCEPT
Function of a Function
3
Write the following as a single rational expression.
RATIONALE
Just as with numeric fractions, we can re-write division of algebraic fractions as multiplication and
multiply across numerators and denominators. To re-write fraction division as multiplication, re-write
the second fraction as its reciprocal (flipping the numerator and denominator).
changes to and division changes to multiplication. We can now multiply across the
numerators and denominators.
x
f left parenthesis x right parenthesis
x
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times is equal to and times is equal to . Next, find any common factors in
the numerator and denominator.
Both the numerator and denominator have a factor of . We can cancel out these factors and
simplify.
Once all common factors have been canceled out in the numerator and denominator, write the fraction
in simplest form.
This is the the simplified fraction written as a single rational expression.
CONCEPT
Multiplying and Dividing Rational Expressions
4
Suppose , , and .
Find the value of the following expression.
RATIONALE
This question involves several properties of logarithms. The Quotient Property of
Logs states that division inside a logarithm can be expressed as subtraction of
individual logarithms.
This means we can express as . Next, the Product
x squared
x
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Property of Logs states that multiplication inside a logarithm can be expressed as
addition of individual logarithms.
This means we can express as . Then, the Power
Property of Logs states that exponents inside a logarithm can be expressed as
outside scalar multiples of the logarithm.
This means we can express as and as .
Finally, we can substitute the values we were previously given for
,
, and
.
Recall that , , and . Once these given values are
substituted into the expression, simplify each term and then perform the addition
and subtraction.
times is , and times is . Finally, add these values together.
The logarithmic expression evaluates to .
CONCEPT
Applying Properties of Logarithms
5
Solve the following logarithmic equation.
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