(e) When will the insect population double? 2. Growth of Bacteria The number N of bacteria present in a culture at timet (in hours) obeys the model N (t) = 1000e0.011 (a) Determine the number of bacteria at t = 0 hours. (b) What is the growth rate of the bacteria? (c) What is the population after 4 hours? (d) When will the number of bacteria reach (e) When will the number of bacteria double? Decay Strontium-90 is a radioactive material
(e) When will the insect population double? 2. Growth of Bacteria The number N of bacteria present in a culture at timet (in hours) obeys the model N (t) = 1000e0.011 (a) Determine the number of bacteria at t = 0 hours. (b) What is the growth rate of the bacteria? (c) What is the population after 4 hours? (d) When will the number of bacteria reach (e) When will the number of bacteria double? Decay Strontium-90 is a radioactive material
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Number 2 part e

Transcribed Image Text:### 4.8 Assess Your Understanding
#### Applications and Extensions
1. **Growth of an Insect Population**
The size \( P \) of a certain insect population at time \( t \) (in days) obeys the model \( P(t) = 500e^{0.02t} \).
- (a) Determine the number of insects at \( t = 0 \) days.
- (b) What is the growth rate of the insect population?
- (c) What is the population after 10 days?
- (d) When will the insect population reach 800?
- (e) When will the insect population double?
2. **Growth of Bacteria**
The number \( N \) of bacteria present in a culture at time \( t \) (in hours) obeys the model \( N(t) = 1000e^{0.01t} \).
- (a) Determine the number of bacteria at \( t = 0 \) hours.
- (b) What is the growth rate of the bacteria?
- (c) What is the population after 4 hours?
- (d) When will the number of bacteria reach a certain value?
- (e) When will the number of bacteria double?
3. **Radioactive Decay**
Strontium-90 is a radioactive material that decays according to the function \( A(t) = A_0e^{-0.0244t} \), where \( A_0 \) is the initial amount present and \( A \) is the amount remaining at time \( t \).
- (Additional problems or extensions might be included here if relevant.)
4. **Additional Examples**
(Details of additional examples such as radioactive decay calculations, etc.)
5. **Growth of**
(This section appears incomplete and could relate to an additional example or further details on the growth model.)
### Explanation of Diagrams/Graphs
- **No diagrams or graphs are provided in the text.** Any accompanying diagrams would likely illustrate the concepts of growth and decay over time for different biological and chemical processes as mentioned in the text.
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