document.write( "Question 1162793: The size P of a certain insect population at time t​ (in days) obeys the function P(t)=900e^0.03t
\n" ); document.write( "​(a) Determine the number of insects at t=0 days.
\n" ); document.write( "​(b) What is the growth rate of the insect​ population?
\n" ); document.write( "​(c) What is the population after 10​ days?
\n" ); document.write( "​(d) When will the insect population reach 1440?
\n" ); document.write( "​(e) When will the insect population​ double? \n" ); document.write( "
Algebra.Com's Answer #786656 by Boreal(15235)\"\" \"About 
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growth rate is 3% the 0.03 in the e^rt, where r is the rate of growth.
\n" ); document.write( "in 10 days the population is 900*e^0.3=1214.87 or 1215
\n" ); document.write( "reaches 1440 when 1440=900*e^0.03t
\n" ); document.write( "1.6=e^0.03 t
\n" ); document.write( "ln both sides
\n" ); document.write( "0.47=0.03t
\n" ); document.write( "t=15 2/3 days\r
\n" ); document.write( "\n" ); document.write( "doubles in 24 days using the rule of 72, but that is empirical
\n" ); document.write( "2=e^0.03t
\n" ); document.write( "ln2=0.03t
\n" ); document.write( "0.693=0.03t
\n" ); document.write( "t=23.1 days
\n" ); document.write( "Some use the rule of 70, which would give 23.3 days and is a better estimate.
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