Explain why some aren't exponential and some are?

Question

Which scenario would best be modeled by an exponential growth function?

A. A babysitter who gets paid $10 per child.

B. Bacteria in a petri dish that triples every hour.

C. Water in a bucket that is evaporating by half the volume every day.

D. A worker who receives a one-time bonus of 11% of their annual salary.

Answer 1

exponentials are a way of doing lot's of multiplications or divisions really quickly.

For example, I could write 5*5*5*5*5*5*5*5, or I could just do 5⁸.

The exponent is the number of times 1 is being multiplied by the base (in my example, 5).

A 1-time payment does not need an exponential, because you're only multiplying once.

In fact, a recurring payment (like getting $5 per day) doesn't need an exponent either, because you would add those together, not multiply.

Exponents are used when growth builds on itself.

A) the money you make per child never goes up. You would write this as y = 10x, where x is the number of children.

B) Imagine you start out with 1 bacteria. Then you have 3, then 9, then 27, then 81, 243, etc... This would be modeled by y = 3^x, because each out you are multiplying whatever you have by 3, then multiplying THAT by 3, and on and on. X is the number of times you multiply by 3.

C) This is just like the last one, but instead of multiplying by 3, you're dividing by 2. dividing by 2 is the same thing as multiplying by 1/2, so we can model this one as y = (1/2)^x. Each day (x), we are multiplying the amount of water left by 1/2. So x is the number of times we multiply by 1/2.

D) to find a percentage, we multiply the salary by 0.11. However, this is a 1-time payment, so we do not need to use an exponent.

Answer 2

The formula for answer A would be $10 x (# of children) - exponent are all 1

The formula for B would be (# of bacteria at start) x 3 to the power of the number of hours - exponential growth.

For answer C : (volume of water) x 0.5 to the power of the number of days (exponential decay)

For D: Salary x .11 (no exponents)

Choose B.

Feel free to contact me if I can answer any other questions.