$$ 1 \leftarrow $$ The size P of a certain insect population at time t (in days) obeys the function $$ \mathrm{P}(\mathrm{t})=600 e^{0.04 t} $$ (a) Determine the number of insects at $$ \mathrm{t}=0 $$ days. (b) What is the growth rate of the insect population? (c) Graph the function using a graphing utility. (d) What is the population after 10 days? (e) When will the insect population reach 720 ? (f) When will the insect population double?

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It seems that I am unable to generate the graph at this moment. However, you can easily graph the function $$ P(t) = 600 e^{0.04 t} $$ using any graphing utility or software such as Desmos, GeoGebra, or a graphing calculator.

### Summary of Answers:
- (a) The number of insects at $$ t = 0 $$ days is **600**.
- (b) The growth rate of the insect population is **0.04 per day**.
- (c) Graphing the function can be done using graphing software.
- (d) The population after 10 days is approximately **895** insects.
- (e) The insect population will reach 720 in approximately **4.56 days**.
- (f) The insect population will double in approximately **17.33 days**.
- (a) 600 insects at $$ t = 0 $$ days. - (b) Growth rate is 0.04 per day. - (c) Graph the function using a graphing tool. - (d) Population after 10 days is approximately 895 insects. - (e) Population reaches 720 in about 4.56 days. - (f) Population doubles in about 17.33 days.

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