5.      Housing developers hoping to attract buyers will often build in amenities for community members to enjoy. In a particular community, fishing is a key attraction, so the housing developers agree to build a small lake and stock it with trout. The population of trout over time can be modeled by p(t) = `+`(`/`(`*`(1200), `*`(`+`(1, `*`(29, `*`(exp(`+`(`-`(`*`(.36, `*`(t))))))))))); ,   where time is measured in months.  

restart;  

 

p := proc (t) options operator, arrow, function_assign; `+`(`/`(`*`(1200), `*`(`+`(1, `*`(29, `*`(exp(`*`(-1, `*`(.36, `*`(t)))))))))) end proc;  

(8.5.1)
 

 

p(0);  

40.00000000; (8.5.2)
 

 

 

`+`(`*`(`/`(1, 10), `*`(p(15))), `-`(`*`(`/`(1, 10), `*`(p(5)))));  

85.39032448; (8.5.3)
 

 

 

 

(D(p))(8);  

101.8341124; (8.5.4)
 

 

 

 

plot(p(t), t = -100 .. 150);  

Plot_2d
 


 

 

with(Student[Calculus1]); -1 

InflectionPoints(p(t));  

[9.353599528]; (8.5.5)
 

 

p(9.4);  

605.0111345; (8.5.6)
 

 


 

 

 

Asymptotes(p(t));  

[y = 0., y = 1200.]; (8.5.7)