Answer:
a)The linear function for is:
b)The exponential function for is:
Step-by-step explanation:
(a) Suppose that P(t) is a linear function. Find a formula for P(t):
can be modeled by a linear function in the following format.
, in which
is the initial number of bacteria cells in the dish, t is the time and r is the rate that the number decreases.
Since the dish initially contains 2000 bacteria cells,
We have
An antibiotic is introduced and after 4 hour, there are now 1600 bacteria cells present. So . With this information, we can find the value of r.
So, the linear function for is:
b) Suppose that P(t) is an exponential function. Find a formula for P(t)
can also be modeled by an exponential function in the following format:
The values mean the same as in a). We use the fact that to find r.
So, the exponential function for is:
