Question

Each day 1/2 of the money that is in a bank vault is removed. No money is added to the vault. Which of the following models this situation?

A. Linear function with a negative rate of change
B. Linear function with a positive rate of change
C. Exponential Decay function
D. Exponential Growth function

Answer 1

C : Exponential Decay function

Explanation:

So, when you see something like division or multiplication in a graph, it is most likely an exponential graph. In this case we are dividing, by 2 or multiplying by 1/2(the same thing), when you are taking half of something it is less. So this would be an exponential decay(decreasing) function. The opposite of that would be a growth function(postive).

A linear function would have a CONSTANT rate of change, meaning, you are not multiplying or dividing, it is just increasing(positive rate) or decreasing(negative rate) by a certain number.

Example Linear; 4x+5=y; mx+b=y(form)

⇒4 is the constant rate(slope), what is being constantly added.

Exponential example;

⇒ f(x)=
`10(2)^(x)`;(
`ab^(x)` form)

⇒ Growth factor= 2(What we are multiplying by (b in the function))

Key words for each type of function ↓

Linear : Constant, slope, y=mx+b, adding, subtracting, line graph.

↓

Exponential : Growth, decay, % increasing/decreasing, division, multiplication, curved graph, shaped like L.

Therefore, this is an Exponential Decay function

Hope this helps !

Answer 2

Answer: C. Exponential Decay function

Explanation:

We know that In exponential decay, the total value decreases but the ratio of decreasing remains constant over time.

Here the amount in the bank account is decreasing by constant ratio of 1/2, and the amount that decreases is proportional to the money in the account, therefore, it is called exponential decay.

Hence, the given function is an exponential decay function.