Question 1: Calculate the value of y when y = 3 * 2^x for x = 4.

Answer: 48

Question 2: Plot the graph of y = 2^x for x from -2 to 3.

Answer: Students will plot on grid

Question 3: Construct an exponential decay graph for y = 100 * (0.5)^x. Plot points for x = 0, 1, 2, 3.

Answer: y=100, 50, 25, 12.5

Question 4: If a population of 500 grows exponentially at a rate of 10% per year, what will it be after 3 years? Use the formula y = P(1 + r)^t.

Answer: 732.05

Question 5: Identify the mistake: A student plots y = 2^x and labels the graph as exponential decay.

Answer: The student mislabels the graph; y=2^x represents exponential growth, not decay.

Question 6: Solve for x: 80 = 20 * 3^x.

Answer: x = 1

Question 7: A bacteria culture starts with 200 bacteria and halves every hour. How many bacteria will there be after 5 hours?

Answer: 6.25

Question 8: Plot the exponential decay function y = 150 * (0.8)^x for x = 0 to 4.

Answer: y=150, 120, 96, 76.8, 61.44

Question 9: A car's value depreciates by 15% annually. If its initial value is $20,000, what is its value after 2 years? Use the formula y = P(1 - r)^t.

Answer: 14445

Question 10: A student claims that the graph of y = 5 * (1.2)^x always shows decay. Is this true? Explain briefly.

Answer: No, because (1.2)^x shows exponential growth, not decay.

Question 11: Identify and correct the mistake in this statement: 'Exponential decay graphs always decrease and approach zero.'

Answer: Incorrect; exponential decay graphs decrease but never actually reach zero, they approach it asymptotically.

Question 12: Challenge: Derive the formula for exponential decay y = P * (1 - r)^x and explain each part.

Answer: P is the initial amount, r is the decay rate, (1 - r) is the decay factor, x is time in periods.