Question

A culture of bacteria that initially contained 2000 bacteria has a count of 18000 after 2 hrs. Determine the function that expresses the continuous exponential growth of the number of bacteria as a function of time, t, in hours.

Answer 1

y= 8000x + 2000

Explanation:

to find the formula we can use the points given in the question:

the slope:

to get the slope we can take the 2 points, (0,2000) and (2,18000) where x values are time and y values are bacteria

now using slope-intercept form we can get
`(18000-2000)/(2-0)` which gives a slope of 8000 meaning for each hour there are 8000 new bacteria

intercept:

since we start with 2000 bacteria we know this is the y intercept so when x is 0

formula:

y=8000x + 2000