Concept explainers
(a)
A table to show the bacteria population for the first 4 hours
(a)
Answer to Problem 29PPS
Time(hours) t | Bacteria |
0 | 12 |
1 | 36 |
2 | 108 |
3 | 324 |
4 | 972 |
Explanation of Solution
Given:
A scientiost estimates that a bacteria culture with an initial population of 12 will triple every hours.
Concept Used:
Rules of Addition/ Subtraction:
- Two numbers with similar sign always get added and the resulting number will carry the similar sign.
- Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.
Calculation:
In order to make a table of bacteria population
Time(hours) t | Bacteria |
0 | 12 |
1 | 36 |
2 | 108 |
3 | 324 |
4 | 972 |
Thus, the table is above for the population of bacteria every hour
(b)
Which kind of model best represents the data
(b)
Answer to Problem 29PPS
The model is exponential
Explanation of Solution
Given: the table
Time(hours) t | Bacteria |
0 | 12 |
1 | 36 |
2 | 108 |
3 | 324 |
4 | 972 |
Concept Used:
If first difference of y-values is equal, then model be linear
If second difference be equal, then the model be quadratic
If first and second differences are not equal then the model will be exponential
Calculation:
In order to the models we see that in the table there is a constant ratio of 3 and the best models is a exponential function of the form
(c)
The function that models the data
(c)
Answer to Problem 29PPS
The function is
Explanation of Solution
Calculation:
In order to find the function we have constant ratio is 3 so
Thus, the function is
(d)
How many bacteria after 8 hours
(d)
Answer to Problem 29PPS
The number of bacteria after 8 hours is
Explanation of Solution
Calculation:
In order to find the number of bacteria after 8 hours shown below:
Thus, the number of bacteria after 8 hours is
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