Exponential Functions and Applications

These flashcards cover concepts related to exponential growth and decay, including functions, applications, and calculations in different contexts.

What is the doubling time of a bacteria sample that starts with 8 bacteria?

The amount of bacteria doubles every 13 minutes.

If a sculpture bought for $380 increases in value by 8% each year, what is its value in 1990?

The value would be approximately $511.20.

What is the equation for exponential growth?

y = a(1 + r)^t, where a is the starting value, r is the growth rate, and t is time.

In a decay scenario, if a new car starts at $20,000 and loses 16% of its value each year, what is its value after one year?

$16,800.

Define the variable in the exponential function for newly reported HIV cases, where t is the number of years after 2000.

t represents the number of years since 2000.

If the population of a town in 2005 was 25,000, how can you determine the annual growth rate?

Calculate the percent increase in population each year using the population data from 2005 to 2010.

What is the original price of a necklace currently valued at $650 if it increased in value by 3% a year for 15 years?

The original price was approximately $314.55.

What happens to the value of a house that increases by 5% per year, starting at $20,000 in 1950, by 1995?

The value would be approximately $51,791.70.

What does 'r' represent in the context of an exponential growth/decay equation?

'r' is the rate of growth or decay expressed as a decimal.

How do you model the amount of smartphones sold given a growth rate of 32.7% from 2012 to 2013?

Use the formula: Sales in 2018 = 959 million * (1 + 0.327)^(2018-2012).