Two different bacteria are growing in a lab. The following functions represents the bacteria.

Bacteria A: f (x) = 1000. 3^x, where x is number of hours.

Bacteria B: g (x) = 3000. 2^x, where x is number of hours.

Which of the following statements are true? Select all that apply.

() Bacteria B is growing at a fasster rate than Bacteria A.

() Baccteria B started with 3000 bacteria.

() Bacteria A doubles every three hours.

() Bacteria B doubles every hour.

() In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.

Question

Mathematics

Jesse Hatfield

15 August, 11:51

Two different bacteria are growing in a lab. The following functions represents the bacteria.

Bacteria A: f (x) = 1000. 3^x, where x is number of hours.

Bacteria B: g (x) = 3000. 2^x, where x is number of hours.

Which of the following statements are true? Select all that apply.

() Bacteria B is growing at a fasster rate than Bacteria A.

() Baccteria B started with 3000 bacteria.

() Bacteria A doubles every three hours.

() Bacteria B doubles every hour.

() In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.

+3

Answers (1)

Know the Answer?

Margaret Shields · Answer 1

For this case we have a function of the form:

y = A (b) ^ x

Where,

A: initial amount

b: growth rate

x: time

We then have the following functions:

f (x) = 1000. 3 ^ x

g (x) = 3000. 2 ^ x

For x = 3 we have:

f (3) = 1000. 3 ^ 3 = 1000 * 27 = 27000

g (3) = 3000. 2 ^ 3 = 3000 * 8 = 24000

Answer:

the following statements are true:

Baccteria B started with 3000 bacteria

Bacteria B doubles every hour.

In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.