AnalysisPage 1

Exponential Growth and Decay

  1. Silver City’s present population of 1,000 is expected to grow exponentially over the next 10 years at 4% per year continuously. How many people will live in SilverCity at that time?
  1. The value of houses in Longview is said to be growing exponentially at 12% per year. What will a house valued at $100,000 today be worth in 8 years?
  1. The population P of a town is 123,000 and is decreasing at the rate of 2.375% each year. Find the algebraic representation of P as a function of time. Determine when the population will reach 50,000.
  1. Suppose the population of a nation is growing at 3% per year. If the population was at 30,000,000 in 1995, what will the population be in 2005?
  1. If $1500 is invested so that it grows at the rate of 10% per year, what will the investment be worth in 20 years?
  1. The consumer price index (CPI) is a measure of goods and services. The U.S. government set the index at 100 for 1967, the base year. In 1977, the index was 181.5. What was the average annual rate of increase over the decade from 1967 to 1977?
  1. A golf ball is dropped onto a hard surface from a height of 12 feet, and it bounces up and down. At each bounce, the ball loses 18% of its previous height.

a) How high will the ball bounce after the 5th bounce?

b) How long before the ball rises no higher than 1 inch?

  1. If grocery prices increase 1% a month for a whole year, how much would groceries that cost $100 at the beginning of the year cost at the end of the year.
  1. At the start of an experiment, 2000 bacteria are present in a colony. 3 hours later, the population is 3800.

a)Find the exponential function that represents this growth pattern.

b) Determine the population 5 hours after the start of the experiment.

c) When will the population reach 10,000?

Exponential Growth Decay 2Mr. John Cendrowski

Lower Moreland HS