Answer:
(c) and (e) are true
Step-by-step explanation:
Given
[tex]P(d) = 10. (1.08)^d[/tex]
See attachment for complete question
Required
Which of the options is true
(a) 1080 insects on day 1
This implies that d = 1
So, we have:
[tex]P(1) = 10* (1.08)^1[/tex]
[tex]P(1) = 10* 1.08[/tex]
[tex]P(1) = 10.8[/tex]
(a) is incorrect because [tex]P(1) \ne 1080[/tex]
(b) 10800 insects after a week
This implies that [tex]d = 7[/tex]
So, we have:
[tex]P(7) = 10* (1.08)^7[/tex]
[tex]P(7) = 10* 1.71382426878[/tex]
[tex]P(7) = 17.14[/tex]
(b) is incorrect because [tex]P(7) \ne 10800[/tex]
(c): Growth factor per day is 1.08
An exponential factor is represented as:
[tex]y = ab^x[/tex]
Where
b is the growth factor
By comparison:
[tex]b = 1.08[/tex]
Hence, (c) option is true
(d): Growth factor per week is 1.08*7
In (c), we have:
[tex]b = 1.08[/tex] as the daily growth factor
So, the growth factor for n days is:
[tex]Factor = 1.08^n[/tex]
Substitute 7 for n i.e. 7 days
[tex]Factor = 1.08^7[/tex]
So, the growth factor for 7 days is: [tex]1.08^7[/tex] not [tex]1.08*7[/tex]
Hence, (d) option is true
(e): Growth factor per week is 1.08*7
In (c), we have:
[tex]b = 1.08[/tex] as the daily growth factor
For hourly rate, we have:
[tex]Factor = 1.08^\frac{1}{24}[/tex]
Hence, (e) option is true
