Question

A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256 mm2, and the bacterial culture stops growing when it covers this area. The area in mm2 that the bacteria cover each day is given by the function ƒ(x) = 2x. What is a reasonable domain for this function?

Answer 1

domain is [0,8]

Explanation:

A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256 mm2, and the bacterial culture stops growing when it covers this area. The area in mm2 that the bacteria cover each day is given by the function ƒ(x) = 2^x

Area = 2^x

256= 2^x

2^8 = 2^x

x=8

domain start at x=0 and end at x=8

So domain is [0,8]

Answer 2

x ∈ [0,8]

Explanation:

We need to find the value of x such that

2^x = 256

We know that

256 = 2^8

Therefore

2^x = 2^8

Since both sides of the equation have the same base, it must mean that

x = 8

So,

ƒ(8) = 2^(8) = 256 mm^2

The domain of the function is

x ∈ [0,8]