Exploring Exponential Functions and Their Applications

This video tutorial covers exponential functions, including transformations, graphing, and identifying domain and range. It explains exponential growth and decay, compound interest, and solving related word problems. The tutorial also introduces geometric sequences, detailing recursive and explicit formulas.

What does a negative 'a' value indicate in an exponential function's transformation?

• Vertical stretch

• Reflection

• Horizontal shift

• Vertical shrink

How is the domain of an exponential function like y=1/2^(x-1)+2 described?

• All positive numbers

• All negative numbers

• All real numbers

• Numbers greater than 0

What is the range of the given exponential function?

• y < 2

• y >= 2

• y > 2

• y = 2

What does the compound interest formula calculate?

• Principal amount after a certain period

• Monthly interest payments

• Total interest earned

• Annual interest rate

After 3 years, how much interest is earned on a $50 deposit with 0.05% interest compounded monthly?

• $0.76

• $0.75

• $0.50

• $1.00

What is the value of a car after 5 years if it depreciates 14% annually from an initial value of $11,950?

• $6,000.00

• $11,000.00

• $10,000.00

• $5,621.60

How much did a house appreciate in value after 16 years if it was initially worth $180,000 and appreciated 4.86% annually?

• $384,618.49

• $200,000.00

• $300,000.00

• $500,000.00

What is the common ratio in a geometric sequence where each term is half of the previous term?

• 0

• -1/2

• 1/2

• 2

What is the first term of the geometric sequence where the first term is 400 and each subsequent term is halved?

• 50

• 100

• 200

• 400

What formula represents the explicit formula for a geometric sequence?

• a_m = a_1 + r(n - 1)

• a_m = a_1 / r^(n - 1)

• a_m = a_1 * r^(n - 1)

• a_m = a_1 - r^(n - 1)