Question

A colony of bacteria has 10,000 bacteria and is growing exponentially. The inequality 10,000(4x) ≥ 320,000 represents the hours, x, for which the colony will have at least 320,000 bacteria.
Which interval represents the hours when the colony will have at least 320,000 bacteria?


[2.5, ∞)

[3, ∞)

[32, ∞)

[0, 2.5]

I have no clue what it is

Answer 1

Answer:

The correct option is;

[2.5, ∞)

Step-by-step explanation:

The given exponential equation can be expressed as follows;

10,000 × 4ˣ ≥ 320,000

Therefore we have;

4ˣ ≥ 320,000/10,000

4ˣ ≥ 32

㏒(4ˣ) ≥ ㏒(32)

x·㏒4 ≥ ㏒(32)

x ≥ ㏒(32)/㏒4

∴ x ≥ 2.5

Therefore, the interval the colony will have at least 320,000 bacteria is where x ≥ 2.5 or 2.5 ≤ x < ∞ which gives, the interval  [2.5, ∞)