writing an equation that models exponential growth or decay

Question

To begin a bacteria study, a petri dish had 2300

 bacteria cells. Each hour since, the number of cells has increased by 11%

.Let t

 be the number of hours since the start of the study. Let y

 be the number of bacteria cells.Write an exponential function showing the relationship between y

 and t

.

Answer 1

There is more than one way to get an exponential function out of the information given. The way the question is worded, however, seems to suggest the following type of answer:

One general form of exponential function is y = a·b^x, where a is the initial value, and b is the growth or decay factor. So right away we can say that a = 2300.

Now for the growth factor. When something is increasing or decreasing by a certain percentage, we are adding or subtracting that percentage to the 100% (which is equal to 1) that exists currently. So here we're increasing by 11%, or 0.11. Then the growth factor b is (1 + 0.11), or 1.11.

So we put it all together, and we get y = 2300·1.11^x.

Answer 2

The basic form of an exponential equation is:

y = a·(1+r)^t where:

1. y = the number of bacteria at time t
2. a is the starting number of bacteria = 2300
3. r = the growth or decay rate expressed as a decimal = 11% = 0.11
4. t = time (hours)

y = a·(1+r)^t

y = 2300·(1 + 0.11)^t

y = 2300·(1.11)^t