Exponential Functions and Decay Rates

The video tutorial explains exponential growth and decay, focusing on identifying these in equations and solving related word problems. It covers the basic formula Y = a(1 + r)^T, where 'a' is the initial value, 'r' is the growth or decay rate, and 'T' is the time period. Examples include calculating growth and decay in various scenarios, such as investments, deer population, and mice population doubling. The tutorial emphasizes understanding the difference between growth and decay rates and applying the formula to real-world problems.

What is the initial value in an exponential function?

• The coefficient of the exponent

• The base of the exponent

• The starting amount

• The rate of change

In an exponential function, if 1 + r is greater than 1, what does it indicate?

• No change

• Exponential growth

• Linear growth

• Exponential decay

What is the growth rate if the function is Y = 12 * 1.73^T?

• 173%

• 1.73%

• 73%

• 12%

In the function Y = 18 * 0.79^X, what does 0.79 represent?

• Growth rate

• Decay factor

• Time period

• Initial value

How can the decay rate be expressed if the function is Y = 18 * 0.79^X?

• 79% decay

• 79% growth

• 21% decay

• 21% growth

What is the growth rate in the function Y = 197 * 2.5^T?

• 1.5%

• 250%

• 150%

• 50%

If an investment decreases by 15% per year, what is the decay factor?

• 1.85

• 0.85

• 1.15

• 0.15

How much money will be left after 6 months if $119,000 is invested with a 15% annual decay?

• $7,166

• $10,000

• $19,000

• $15,000

What is the initial deer population in the Pacific Grove problem?

• 6,501

• 6,500

• 7,000

• 5,000

What is the growth rate of the deer population per year?

• 77%

• 100%

• 200%

• 177%