Ma1310: Week 1 Exponential and Logarithmic Functions
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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? It is constant raised to the power. 2. What is the natural exponential function? In mathematics, the exponential function is the function e, where e is the number such that the function e is its own derivative http://en.wikipedia.org/wiki/Natural_exponential_function 3. Evaluate 4–1.5 using a calculator. Round your answer to three decimal places.0.120 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?591229.78 5. Write 6 = log2 64 in its equivalent exponential form. 2^6=64 6. Write 8y = 300 in its equivalent logarithmic form. log(base 8) 300 = y 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