1.      State in a few words, what is an exponential function?  2.      What is the natural exponential function?3.      Evaluate 4–1.5…

1.     
State in a few words, what is an exponential function?
 

2.     
What is the natural exponential function?

3.     
Evaluate 4–1.5 using a calculator. Round your answer to three decimal places.

4.     
The formula S = C (1 + r)^t models inflation, where

C = the value today

r = the annual inflation rate

S = the inflated value t years from now

 

Use this formula to solve the following problem:

If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years?

5.     
Write 6 = log2 64 in its equivalent exponential form.

6.     
Write 8y = 300 in its equivalent logarithmic form.

7.     
Hurricanes are some of the largest storms on earth. They are very low pressure areas with diameters of over 500 miles. The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is modeled by the formula f(x) = 0.48 ln (x + 1) + 27.

(Source: A. Miller and R. Anthes, Meteorology)

a.     
Evaluate f(0) and f(100). Interpret the result.

b.     
At what distance from the eye of the hurricane is the air pressure 28 inches of mercury?

8.     
Describe the quotient rule for logarithms and give an example.

9.     
Use properties of logarithms to expand the following:

Log(x/1000)

 

Submission Requirements:
Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab1.1_Date.

 

Evaluation Criteria:

·        

Did you show the appropriate steps to solve the given problems?

·         Did you support your answers with appropriate rationale wherever applicable?

·         Were the answers submitted in an organized fashion that was legible and easy to follow?

 

·         Were the answers correct?

MA1310: Week 1 Exponential and Logarithmic Functions

This lab requires you to:

· Evaluate exponential functions.

· Graph exponential functions.

· Evaluate functions with base e.

· Change from logarithmic to exponential form.

· Change from exponential to logarithmic form.

· Evaluate logarithms.

· Use basic logarithmic properties.

· Graph logarithmic functions.

· Find the domain of a logarithmic function.

· Use common logarithms.

· Use natural logarithms.

· Use the product rule.

· Use the quotient rule.

· Use the power rule.

· Expand logarithmic expressions.

· Condense logarithmic expressions.

· Use the change-of-base property.

Answer the following questions to complete this lab:

1. State in a few words, what is an exponential function? The Exponential function f with base b is defined by f(x) = bx or y = bx,

Where b is a positive constant other than 1 (b > 0 and b ≠ 1) and x is any real number.

2. What is the natural exponential function?

3. Evaluate 4–1.5 using a calculator. Round your answer to three decimal places.

4. The formula S = C (1 + r)^t models inflation, where

C = the value today

r = the annual inflation rate

S = the inflated value t years from now

Use this formula to solve the following problem:

If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years?

5. Write 6 = log2 64 in its equivalent exponential form.

6. Write 8y = 300 in its equivalent logarithmic form.

7. Hurricanes are some of the largest storms on earth. They are very low pressure areas with diameters of over 500 miles. The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is modeled by the formula f(x) = 0.48 ln (x + 1) + 27.

(Source: A. Miller and R. Anthes, Meteorology)

a. Evaluate f(0) and f(100). Interpret the result.

b. At what distance from the eye of the hurricane is the air pressure 28 inches of mercury?

8. Describe the quotient rule for logarithms and give an example.

9. Use properties of logarithms to expand the following:

Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab1.1_Date.
Evaluation Criteria:
· Did you show the appropriate steps to solve the given problems?
· Did you support your answers with appropriate rationale wherever applicable?
· Were the answers submitted in an organized fashion that was legible and easy to follow?
· Were the answers correct?

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log()
1000
x