A laboratory models the population of microorganisms in a culture with the function below, where is the estimated population, in thousands of microorganisms, days after monitoring begins.
Which choice gives the model's estimated average decrease in the population per hour?
For a linear function with a transformed input, do not treat the coefficient outside the parentheses as the complete rate automatically. First determine how much the expression inside the parentheses changes when the input increases by one unit. Then multiply by the outside coefficient and carefully convert any output or time units requested in the question.
Hints
Track a one-day change
Consider what happens to the expression when increases by .
Use the output units
The function output is in thousands of microorganisms, so convert the rate to individual microorganisms before converting days to hours.
Convert the time unit
After finding the decrease per day, divide by the number of hours in one day.
Desmos Guide
Use a one-day comparison
Algebra is fastest because the model is already in a form that shows the rate factors. For a Desmos verification, enter .
Check consecutive days
Use a table to evaluate the model at and . The output decreases by , which represents thousand microorganisms in one day.
Convert the verified rate
Multiply the decrease of by to convert from thousands to microorganisms, then divide by to convert from a daily rate to an hourly rate.
Step-by-step Explanation
Find the daily rate of change
When increases by day, increases by . Therefore, the change in is
The population decreases by thousand microorganisms per day.
Convert thousands per day to microorganisms per hour
A decrease of thousand is a decrease of microorganisms per day. Since there are hours in a day,
So the estimated decrease is microorganisms per hour.