Exponential Functions & Geometric Sequences

Which of the following is an example of an exponential function?

Answer explanation

The correct choice is y = 3^x because it represents an exponential function where the variable x is in the exponent position.

• Shift 3 units up

• Shift 3 units down

• Shift 3 units to the right

• Shift 3 units to the left

Answer explanation

The graph shifts 3 units to the left when the exponent is changed to x + 3, indicating a horizontal shift to the left.

If a population of bacteria doubles every hour, starting with 100 bacteria, how many bacteria will there be after 5 hours?

• 500

• 1600

• 3200

• 6400

Answer explanation

Starting with 100 bacteria, the population doubles every hour, so after 5 hours, there will be 100*2^5 = 3200 bacteria. Therefore, the correct answer is 3200.

A radioactive substance decays at a rate of 5% per year. If the initial amount is 200 grams, what will be the amount after 3 years?

• 172.76 grams

• 185 grams

• 150 grams

• 100 grams

Answer explanation

The amount after 3 years can be calculated as 200 * (1 - 0.05)^3 = 172.76 grams, so the correct answer is 172.76 grams.

Which of the following sequences is a geometric sequence?

• 2, 4, 6, 8, 10

• 3, 9, 27, 81

• 1, 3, 5, 7, 9

• 10, 5, 0, -5

Answer explanation

The sequence 3, 9, 27, 81 is a geometric sequence because each term is obtained by multiplying the previous term by 3, making it follow the pattern of a geometric sequence.

What is the 4th term in the geometric sequence 5, 15, 45, ...?

• 135

• 150

• 165

• 180

What is the common ratio of the geometric sequence 2, 6, 18, 54, ...?

• 2

• 3

• 4

• 6

If a car's value decreases by 20% each year, and the car is initially worth $25,000, what will its value be after 2 years?

• $16,000

• $20,000

• $15,000

• $10,000

What is the equation of an exponential function that passes through the points (1, 2) and (3, 8)?

• Reflection across the x-axis

• Reflection across the y-axis

• Vertical stretch

• Horizontal compression