Question

Let the function P represent the population P(d), in thousands, of a colony of insect

Answer 1

Answer:

(c) and (e) are true

Step-by-step explanation:

Given

$P(d) = 10. (1.08)^d$

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:

$P(1) = 10* (1.08)^1$

$P(1) = 10* 1.08$

$P(1) = 10.8$

(a) is incorrect because $P(1) \ne 1080$

(b) 10800 insects after a week

This implies that $d = 7$

So, we have:

$P(7) = 10* (1.08)^7$

$P(7) = 10* 1.71382426878$

$P(7) = 17.14$

(b) is incorrect because $P(7) \ne 10800$

(c): Growth factor per day is 1.08

An exponential factor is represented as:

$y = ab^x$

Where

b is the growth factor

By comparison:

$b = 1.08$

Hence, (c) option is true

(d): Growth factor per week is 1.08*7

In (c), we have:

$b = 1.08$ as the daily growth factor

So, the growth factor for n days is:

$Factor = 1.08^n$

Substitute 7 for n i.e. 7 days

$Factor = 1.08^7$

So, the growth factor for 7 days is: $1.08^7$ not $1.08*7$

Hence, (d) option is true

(e): Growth factor per week is 1.08*7

In (c), we have:

$b = 1.08$ as the daily growth factor

For hourly rate, we have:

$Factor = 1.08^\frac{1}{24}$

Hence, (e) option is true