Question

The doubling time of a population of grasshoppers is 10 days. By what factor does the population of grasshoppers grow in 35 days?

Answer 1

So in 10 days the grasshopper (x) is doubled (2x)
20 days it is 2(2x) or 4x
30 days it is 2(4x) or 8x
in 35 days it is 1/2 of 10 so 1/2 times 2 times 8x=8x

it increased by a factor of 8

Answer 2

The correct answer is:

11.3

Explanation:

In 10 days, the population x would double, becoming 2x.

Every 10 days after, the population would double again. This means at 20 days, the population would be 2(2x) = 4x, and at 30 days, the population would be 2(4x) = 2(2(2x)) = 8x.

Writing the repeated multiplication out, we see that this can be represented with exponents. 10 days would be 2¹(x); 20 days would be 2²(x); 30 days would be 2³(x).

5 days would not be adding a whole number to the exponent, as it is only half of the time it takes to double. This means we would add 0.5 to the exponent; this would make 35 days

$2^{3.5}(x)$, which comes out to 11.3x. This means it increases by a factor of 11.3 in 35 days.