Question

The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteria after 9 hours? graph of a curve passing through the points zero comma 1, one comma two, two comma four, and three comma eight Courtesy of Texas Instruments 128 256 512 1,024

Answer 1

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial population of bacteria

b: growth rate

x: number of hours

Since the diameter is double every hour, then:

$b = 2$

We must now look for the value of A.

To do this, we evaluate an ordered pair of the graph:

For (1, 2):

$2 = A * (2) ^ 1$

Clearing A we have:

$2 = A * 2$

$A = \frac{2}{2}\\A = 1$

Then, the function is given by:

$y = 1 * (2) ^ x$

For after 9 hours we have:

$y = 1 * (2) ^ 9\\y = 512$

Answer:

the diameter of the bacteria after 9 hours is:

$y = 512$