Question

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.

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.