The function models the size of a bacterial culture, in thousands of bacteria, hours after the culture is introduced into a petri dish, where .
What is the best interpretation of the statement " is approximately equal to " in this context?
In function notation, the number in parentheses is the input, and the function's value is the output. For a real-world model, attach the input's and output's units before comparing choices. Evaluate a given function in Desmos if you need its value, then convert any scaled unit. The output is an amount present, not automatically an amount gained.
Hints
- Hint 1
In function notation, the number inside parentheses is the input. Since measures hours after the culture is introduced, what time does the in name?
- Hint 2
The function's output is measured in thousands of bacteria. Once you've evaluated , convert that output to individual bacteria. Is it the whole culture at that time or only the increase since hour ?
Step-by-step
Evaluate the function and read its units
Step 1Identify the time in the function
The in is the input, so it replaces in the rule. Since counts hours after introduction, this gives the culture's size 3 hours later: .
- Step 2
Evaluate the culture size
Type , then in Desmos. It shows . That's the model's output in thousands of bacteria, not the number added since the culture began.
- Step 3
Convert the output to bacteria
The output is in thousands of bacteria, so about in that unit means . That number is the culture's size at hour , not how much it grew since introduction. The dish is predicted to contain about bacteria after hours. Choice A.