Question

A population of bacteria triples every hour. Is this situation linear or exponential? A. Linear, because the function increases by a constant amount B. Exponential, because the function decreases C. Exponential, because the function grows by a common factor D. Linear, because the function increases

Answer 1

it is linear because it has a fixed equation

Answer 2

C. Exponential, because the function grows by a common factor

Explanation:

Given : A population of bacteria triples every hour.

To Find: Is this situation linear or exponential?

Solution:

A linear function : the rate of change is constant.

In an exponential function the rate of change is not constant. there is common growth or decay factor

Since we are given that A population of bacteria triples every hour.

So, there is a growth rate factor i.e. 3

General exponential function:
`y=ab^x`

where a is the initial amount

b is the growth rate factor

So, The Function for given situation :
`y=a(3)^x`

Thus this situation is exponential because the function grows by a common factor.

Hence Option C is correct.