Respuesta :
Answer:
The number of weeks it will take for the beetle population to reach 236 is 28.75.
Step-by-step explanation:
If a quantity starts at size P₀ and grows by d every time period, then the
quantity after n time periods can be determined using explicit form:
[tex]P_{n} = P_{0} + d \cdot n[/tex]
Here,
d = the common difference, i.e. the amount that the population changes each time n is increased by 1.
In this case it is provided that the original population of beetle was:
P₀ = 6; (week 0)
And the population after 8 weeks was,
P₈ = 86
Compute the value of d as follows:
[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]
Thus, the explicit formula for the beetle population after n weeks is:
[tex]P_{n}=P_{0}+8n[/tex]
Compute the number of weeks it will take for the beetle population to reach 236 as follows:
[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]
Thus, the number of weeks it will take for the beetle population to reach 236 is 28.75.
