Question

1. to answer this question more precisely, it would be helpful if we can write a function for the bacteria count in terms of the number of days since monday at 8 am. to do this, it is helpful to look for a pattern. however, if you calculated the bacteria count for each number of days in the table, then the process you used to get the number of bacteria is probably camouflaged; this means it may be difficult to identify a pattern that can lead you to a generalized expression. instead, consider writing the number of bacteria for each number of days in terms of 1500, the initial bacteria count. ask yourself: if you began with a count of 1500 bacteria, how do you get the number of bacteria after 1 day? do you see this is 15002? then the number after 2 days is found by doubling the number of bacteria after 1 day so we now have (15002)2. then the number after 3 days is found by doubling the number after 2 days so we have (150022)2. do you see a pattern? as the number of days increases, what stays the same in the expressions for the number of bacteria? what is changing in the expressions for the number of bacteria? 5. use the pattern from problem 3 to write a function p that represents the number of bacteria per cc after t days. (be sure your function gives you the same data you wrote in the table of problem 2.)

Explanation:

Step1: Identify the initial - value and growth - pattern

The initial bacteria count is 1500. The number of bacteria doubles each day.

Step2: Write the general exponential - growth formula

The general form of an exponential growth function is $P(t)=a\cdot b^{t}$, where $a$ is the initial amount and $b$ is the growth factor. Here, $a = 1500$ and $b = 2$.

Answer:

$P(t)=1500\cdot2^{t}$