Exponential and Logarithmic Applications

During this lesson, we will solve real-life problems by writing and

solving logarithmic and exponential equations.

Walking Speed & City Population

As the population of a city increases, the pace of life also increases. The formula

W = .035 ln P + 2.74models average walking speed, W, in feet per second, for a resident of a city where population is P thousand. Find the average walking speed for people living in New York City with a population of 7323 thousand.* Use the same formula to find the average walking speed in Jackson, Mississippi, where the population is 172, 558 (2010).

Walking Speed & City Population

Height and Age

The percentage of adult height attained by a girl who is x years old can be modeled by

f(x) = 62 + 35 log (x-4)where x represents the girl’s age (from 5 to 15) and f(x) represents the percentage of her adult height. Approximately what percentage of her adult height is a girl at age 15?

Height and Age Problems

Alcohol & Risk of a Car Accident

Medical research indicates that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. This risk is modeled by

R = 6 e 1 2.77 x

Where x is the blood alcohol concentration and R, given as a percent , is the risk of having a car accident. What blood alcohol concentration corresponds to a 17% risk of a car accident?

Alcohol & Risk of Car Accident

Note: In PA, it is illegal to drive at a blood alcohol level of 0.08%.

Carbon-14 Dating: The Dead Sea Scrolls

a. Use the fact that after 5715 years, a given amount of carbon-14 will have decayed to half the original amount to find the exponential decay model for carbon-14.

b. In 1947 earthenware jars containing what were known as the Dead Sea Scrolls were found by an Arab Bedouin herdsman. Analysis indicated that the scroll wrappings contained 76% of their original carbon-14. Estimate the age of the Dead Sea Scrolls.

Use A = A0 e kt

Carbon-14 Dating: The Dead Sea Scrolls

Applications with Exponential & Logarithmic Equations WS: 1-11 odd; 14, 20, 21, 22. 22.

Homework