Suppose that a petri dish initially contains 2000 bacteria cells. an antibiotic is introduced and after 4 hour, there are now 1600 bacteria cells present. let p(t) be the number of bacteria cells present t hours after the antibiotic is introduced. (a) (8 points) suppose that p(t) is a linear function. find a formula for p(t) (b) (8 points) suppose that p(t) is an exponential function. find a formula for p(t)

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:

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step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

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step-by-step explanation: