The formula NEXT = 2 • NOW models the number of bacteria in a test tube. There were 10 bacteria in the test tube after the first
2 answers:
Answer:
160 bacteria
Step-by-step explanation:
We can create an exponential function of the form: , where a is the initial value, b is the rate, and x is the time.
Here, a = 10 and b = 2, so our equation is:
We want the number of bacteria present after the fifth hour, or when x = 5, so we have:
There were 160 bacteria.
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We are given a data set and we are asked to write the model that fits the data. We notice that for each step of "x" the values of "y" increase by the same amount. That means that the data follow a linear model, therefore, we will use:
Where:
To determine the slope "m" we will use the following formula:
Where:
Are data points. From the table we choose the following points:
Now, we substitute in the equation for the slope:
Solving the operations:
Therefore, the slope is -7. Substituting in the equation of the line we get:
Now, we substitute one of the points to get the value of "b". We will substitute the value x = -8, y = 47, we get:
Solving the product:
Now we subtract 56 from both sides:
Now, we substitute the value of "b" in the equation of the line:
And thus we get the line equation.
Answer:
b=3
Step-by-step explanation:
If b is inversely proportional to c then
b is 5 when c is 12, means...
From where we obtain the value of k, the constant needed, which is equals to 5*12=60
Now... to find b when c=20, is just a matter of using our known variables.