Number 2 part e ### 4.8 Assess Your Understanding#### Applications and Extensions1. **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.

Answered: Image /qna-images/answer/83b5a6c3-8266-44cd-9fa8-08c2568f5a6b.jpg

(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