Exponential Growth
Exponential growth is a fundamental concept in mathematics and the sciences, describing a phenomenon where a quantity increases rapidly over time, proportional to its current value. This concept finds widespread application in various fields such as finance, biology, and technology. Characterized by a constant growth rate, exponential growth often leads to dramatic changes and can be observed in population dynamics, compound interest calculations, and the proliferation of technological advancements. Understanding exponential growth is crucial for predicting trends, analyzing data, and making informed decisions in a wide range of disciplines.
Questions
- The population of rabbits in East Fremont is 250 in September of 2004, and growing at a rate of 3.5% each month. If the rate of population growth remains constant, determine the month and year in which the rabbit population will double?
- How much interest is earned after 2 years with an initial deposit of $640 and an interest rate of 3%?
- The population of rabbits in East Fremont is 250 in September of 2004, and growing at a rate of 3.5% each month. If the rate of population growth remains constant, determine the month and year in which the rabbit population will reach 128,000?
- How do you determine if the equation #y = 1/2 (5)^x# represents exponential growth or decay?
- After making a deposit, Puja had $264 in her savings account. She noticed that if she added $26 to the amount originally in the account and doubled the sum, she would get the new amount. How much did she originally have in the account?
- A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
- How do you determine if the equation #y = 0.5(4)^x# represents exponential growth or decay?
- How do you determine if the equation # y = 0.84(1.45)^x# represents exponential growth or decay?
- The volume of harvestable timber in a young forest grows exponentially with a yearly rate of increase equal to 3.5%. What percentage increase is expected in 10 years?
- A radioactive substance has a half life of 120 years. Presently, there are 60 grams of the substance. When were 600 grams present?
- According to Population the Bureau, the world population in 2000 was 6.1 billion and increasing at an annual rate of 1.4%. What would the world population be in 2020? What is the exponential function to predict the actual population?
- The population of a cit grows at a rate of 5% each year. The population in 1990 was 400,000. What would be the predicted current population? In what year would we predict the population to reach 1,000,000?
- How do you determine if the equation #f(x) = 3(.11)^x# represents exponential growth or decay?
- If you invest $2000 in a bank offering 10% interest compounded weekly, how do you find the value of your investment after five years?
- In 1992, the city of Chicago had 6.5 million people. In 2000 they project Chicago will have 6.6 million people. If Chicago's population grows exponentially, how many people will live in Chicago in 2005?
- A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 9,000 bacteria. How do you find the number of bacteria after 5 hours?
- How do you determine if the equation #y = 4^x# represents exponential growth or decay?
- How do you determine if the equation #f(x) = 6^x# represents exponential growth or decay?
- The population of the US was 203 million in the year 1970 and 249 million in the year 1990. If it is growing exponentially, what will it be in the year 2030?
- In 1990, the population of the city of Orange was 110,658 and grew to 136,392 in 2008. Assuming exponential growth, what would the population of Orange be in 2030?