ected to decrease by 15 percent eve hefs at the event. 50(0.85)' represent the number of p w. wer the question, let's solve the equ rform one operation to both sides of
ected to decrease by 15 percent eve hefs at the event. 50(0.85)' represent the number of p w. wer the question, let's solve the equ rform one operation to both sides of
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![Right now, five hundred fifty pastry chefs have gathered for a tournament in your hometown, and the
number is expected to decrease by 15 percent every hour. The organizers want to predict when there will
be 50 pastry chefs at the event.
Let h(t) = 550(0.85)' represent the number of pastry chefs at the tournament, where t is the number of
hours from now.
In order to answer the question, let's solve the equation: 50 = 550(0.85)ʻ
1. First, perform one operation to both sides of the equation so that (0.85)' is alone on the right-hand
side. Write your resulting equation below. [Do not use your calculator at any point.]
Equation:
2. Now, apply the natural logarithm to both sides and simplify the right-hand side by using the property
In (m') = bln(m). Write the resulting equation below. [Do not use your calculator at any point.]
Equation:
3. Finally, isolate the variable t.
Answer: t =
hours](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63bbee30-bb30-4176-a66e-fefcba8e1595%2Ffda6e4c4-68c0-4bc9-9129-bf05d7e709d7%2F3vuhr5_processed.png&w=3840&q=75)
Transcribed Image Text:Right now, five hundred fifty pastry chefs have gathered for a tournament in your hometown, and the
number is expected to decrease by 15 percent every hour. The organizers want to predict when there will
be 50 pastry chefs at the event.
Let h(t) = 550(0.85)' represent the number of pastry chefs at the tournament, where t is the number of
hours from now.
In order to answer the question, let's solve the equation: 50 = 550(0.85)ʻ
1. First, perform one operation to both sides of the equation so that (0.85)' is alone on the right-hand
side. Write your resulting equation below. [Do not use your calculator at any point.]
Equation:
2. Now, apply the natural logarithm to both sides and simplify the right-hand side by using the property
In (m') = bln(m). Write the resulting equation below. [Do not use your calculator at any point.]
Equation:
3. Finally, isolate the variable t.
Answer: t =
hours
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