a.
To find: How many people have entered the park by
a.
Answer to Problem 55EP
The number of people entered the park is
Explanation of Solution
Given information:
Calculation:
Given that the rate at which people entered the amusement park is given by,
Integrating the given function,
By substitution method,
To find the new boundaries:
At
At
Now,
Using substitution method,
To find the new boundaries:
At
At
Now,
Applying fundamental theorem of calculus,
Now,
Therefore, the number of people entered the park by
b.
To find: How many dollars are collected from admissions to the park on the same day.
b.
Answer to Problem 55EP
The dollars collected from the admissions to the park is
Explanation of Solution
Given information:
Calculation:
Given that the rate at which people entered the amusement park is given by,
Integrating the given function,
By substitution method,
To find the new boundaries:
At
At
Now,
Using substitution method,
To find the new boundaries:
At
At
Now,
Applying fundamental theorem of calculus,
Now,
The total cost is calculated by,
Therefore, the dollars collected from the admissions to the park is
c.
To find: The value of
c.
Answer to Problem 55EP
The value of
Explanation of Solution
Given information:
Calculation:
It is known that,
At
According to this, the number of persons in the park at
In this instance, the population is now dropping at a rate of roughly
d.
To find: The value of time
d.
Answer to Problem 55EP
The value of time
Explanation of Solution
Given information:
Calculation:
When the rate of change equals zero, as shown in the equation below, the number of persons in the park is at its highest.
Multiply the equation by its least common denominator (LCD). For the equation above,
Using
The standard form is given by,
The quadratic formula is given by,
Dividing on both sides by
The period when the number of persons is at its peak is
Therefore, the value of time
Chapter 7 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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