Writing Exponential Functions from Real World Scenarios

The video tutorial explains how to write exponential functions from word problems, focusing on identifying the initial value 'a' and the growth or decay rate 'b'. It provides examples, including radioactive decay, car depreciation, bacteria growth, and a baseball card collection, to illustrate how to determine 'b' and apply exponential functions to solve real-world problems.

What does the variable 'a' represent in the exponential function formula?

• Initial value

• Time period

• Decay rate

• Growth rate

If an element has a half-life, what would be the value of 'b' in the exponential function?

• 0

• 1

• 0.5

• 2

How do you calculate the new value of a decaying element after a certain number of years?

• Add the decay rate to the initial value each year

• Subtract the decay rate from the initial value each year

• Divide the initial value by the decay rate

• Multiply the initial value by the decay rate raised to the power of years

What is the decay rate if a car's value goes from $28,200 to $26,508 in one year?

• 1.94

• 0.06

• 1.06

• 0.94

How much will the car be worth after seven years, starting from $30,000?

• $30,000

• $26,508

• $28,200

• $19,454.33

What is the growth rate if the number of bacteria increases from 20 to 22 in one hour?

• 0.1

• 2.2

• 1.0

• 1.1

How many bacteria will there be after 12 hours, starting from 20?

• 62.77

• 32

• 44

• 24

If a collection triples each year, what is the value of 'b'?

• 3

• 0.33

• 1

• 2

Starting with 25 baseball cards in 2021, how many cards will there be in 2026?

• 75

• 100

• 6700

• 125

What does the exponential function y = 25 * 3^x represent?

• Growth of a collection

• Halving of a collection

• Constant collection size

• Decay of a collection