Question 45 1 pts A population of flies decreases according to the function rule $f(x) = 725(0.85)^x$, where $x$ represents the number of hours after their food source becomes depleted. Determine the end behavior of this function as $x \to \infty$ and what it means in the context of the problem. $f(x) \to 616.25$ as $x \to \infty$: The population of flies decreases to about 616. $f(x) \to 142.734$ as $x \to \infty$: The population of flies begins with about 142 flies. $f(x) \to 0$ as $x \to \infty$: The population of flies approaches zero as time goes on. $f(x) \to \infty$ as $x \to \infty$: The population of flies continues to increase as time goes on.
Added by Garrett F.
Close
Step 1
85)^t\), where \(t\) represents the number of hours after their food source becomes depleted. As \(t\) approaches infinity (\(t \to \infty\)), the term \((0.85)^t\) will approach 0 because 0.85 is between 0 and 1. Show moreβ¦
Show all steps
Your feedback will help us improve your experience
Daniel Carr and 82 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A biologist has determined that the maximum number of fruit flies that can be sustained in a carefully controlled environment (with a limited supply of space and food) is 960. Suppose that the rate at which the population of the colony increases obeys the rule: dQ/dt = kQ(C - Q) where C is the carrying capacity (960) and Q denotes the number of fruit flies in the colony at time t. If the initial population of fruit flies in the experiment is 30 and it grows to 139 after 10 days, determine the population of the colony of fruit flies at the end of the 20th day. (Round your answer to the nearest whole number.)
Suman K.
Shaiju T.
Exploration 15.2: The Logistic Growth Model PROBLEM: Fruit flies are situated in a small glass bottle containing a limited amount of food. Suppose the fruit fly population after t days is given by the function P(t) = 230 / (1 + 56.5e^-(.0016)(230)t) 1. How many fruit flies were originally placed in the bottle? 2. What is the carrying capacity of the small glass bottle as t gets larger (graph this function to help answer this question)? 3. When will the population of fruit flies be 200? 4. Using a graphing utility, change the various constants in the fruit fly equation one at a time and notice how each affects the characteristic "S" shape of the logistic function graph.
David S.
Recommended Textbooks
Precalculus with Limits
Precalculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD