Question

A population of beetles is growing according to a linear growth model. The initial population was 3 beetles, and the population grew to 67 beetles after 8 weeks. Determine the beetle population after 30 weeks.

Answer 1

Let's first determine the formula of the linear growth of the beetles:

Given,

Initial population = 3 Beetles

Population after 8 weeks = 67 Beetles

Let,

y = Population of the Beetles

x = No. of weeks

b = Initial number of Beetles

m = rate of growth

We get,

`\text{ y = mx + b}`

Let's determine the rate of growth (m) of the beetles when after 8 weeks it has a population of 67 beetles.

`\text{ y = mx + b }\rightarrow\text{ 67 = m(8) + 3}`
`\text{ 67 = 8m + 3 }\rightarrow\text{ 8m = 67 - 3 }\rightarrow\text{ 8m = 64}`
`\text{ m = }(64)/(8)\text{ }\rightarrow\text{ m = 8}`

Therefore, the rate of growth of the beetles per week is 8 Beetles per Week.

Let's determine the beetle population after 30 weeks:

`\text{ y = mx + b }\rightarrow\text{ y = (8)x + 3}`
`\text{ y = 8x + 3}`

After 30 weeks,

`\text{ y = 8(30) + 3 = 240 + 3}`
`\text{ y = 243}`

Therefore, after 30 weeks, the beetle population will be 243.

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