Question

Consider the exponential function g(x)=100•(2)^x. Which of the following situations could be modeled by the function? SELECT ALL THAT APPLY.
A) a 100in. Tall fruit tree doubles in height each year.

B) 100 people are infected with a virus. Every day, 2 more people are infected.

C) there are 100 bacteria in a culture. The amount doubles every 5 hours.

D) there is $100 in a saving account. An additional $100 is added to the account every month.

E) 100 wolves are reintroduced to Yellowstone national park. Each year, the number of wolves double.

Answer 1

Answer: On Algebra Nation A,C,E is right

Step-by-step explanation:

Answer 2

Exponential functions model exponential increase/decrease; in this case, we must understand that exponential functions differ from linear functions, which increase, well, linearly: the function can be represented by a straight line. In real-world terms, that means stuff increases/decreases constantly, not at a changing rate.

For this question, (B) and (D) are not modeled by g(x) because they increase linearly: a set amount of things happen per unit of time.

So, (A), (C), and (E) can be modeled by exponential functions because they double per time unit. However, (C) is not modeled by g(x) because it doubles every 5 hours (time units). If we look at g(x), it doubles every time unit (2^x, where x is the time unit). (A) and (E) double every time unit (every year), while C doubles every 5 time units (every 5 hours).

So, your answer would be (A) and (E).

Short note: What does g(x) actually mean?

Well, 100 represents the initial input: whether that be height, money, or population. That's your starting value you base your function off of.
2 is the base: how much your input changes exponentially: 2 is doubling, 3 is tripling, etc. Similarly, 0.5 is halving, and so on.
As x is the exponent, it tells you how long it takes for your input to change by the base: 1x is per 1 time unit, 0.5x is per 2 time units, 0.25 is per 4 time units, and so on. Conversely, 2x is per 0.5 time units, 4x is per 0.25 time units, and so on.
This is because, for 0.5x, it takes us double the time (2 time units) for the input to change by the base. Similarly, for 2x, it only takes us half the time (0.5 time units) for the input to change by the base.
If you are able to apply this understanding to exponential functions like g(x), you can understand what they represent, and what they can model. Similarly, you can look at worded examples of exponential functions and see how they could be represented mathematically. That's the most important thing to learn.