QuestionEach question is worth 3 marks (one mark for correct answer, two marks for
6. The population of a pod of whales has tripled in size recently over an 11year period. They have a current population of 40 individuals. What might the population be after 33 more years?

Studdy Solution

STEP 1

1. The population of the pod of whales triples every 11 years.
2. The current population is 40 individuals.
3. We are tasked with finding the population after 33 more years.

STEP 2

1. Determine the growth factor over the given period.
2. Calculate the number of 11-year periods in 33 years.
3. Apply the growth factor to find the future population.

STEP 3

Determine the growth factor over the given period. Since the population triples every 11 years, the growth factor is 3.

STEP 4

Calculate the number of 11-year periods in 33 years. Divide 33 by 11:
$\text{Number of periods} = \frac{33}{11} = 3$

STEP 5

Apply the growth factor to find the future population. Since the population triples every 11 years, and there are 3 such periods in 33 years, the population will be:
$\text{Future population} = 40 \times 3^3$
Calculate $3^3$ :
$3^3 = 3 \times 3 \times 3 = 27$
Now multiply by the current population:
$\text{Future population} = 40 \times 27 = 1080$
The population after 33 more years is:
$\boxed{1080}$

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