Question

9 : a population of insects increases at the rate of 200 10t 13t2 what is the change in the population of insects between day 0 and day 3?

Answer 1

The change in population of insects between day 0 and day 3 is 199,683.

Step-by-step explanation:

To find the change in population of insects between day 0 and day 3, we can use the formula for population growth rate: change in population = population growth rate * (final time - initial time).

In this case, the population growth rate is given as 200 * 10t - 13
`\rm t^2` . Plugging in the values for t=0 and t=3, we get:

change in population = 200 *
`10^3`- 13(
`3^2` ) - 200 *
`10^0` - 13(
`0^2`)

= 200 * 1000 - 13 * 9 - 200 * 1 - 13 * 0

= 200000 - 117 - 200 + 0

= 199683

Therefore, the change in population of insects between day 0 and day 3 is 199,683.

Answer 2

The change in the population of insects between day 0 and day 3 is 199683, calculated using the growth rate function
`200 * 10^t - 13t^2` evaluated at t=0 and t=3.

Step-by-step explanation:

The subject of this question is Mathematics, specifically related to exponential growth and population dynamics. To calculate the change in the population of insects between day 0 and day 3, we need to evaluate the given population growth function at day 0 and day 3 and then find the difference. The growth rate function provided appears to be
`200 * 10t - 13t^2`, where t represents time in days.

At day 0 (t=0):

Population change = 200 × 100 - 13 × 02 = 200 × 1 - 0 = 200

At day 3 (t=3):

Population change = 200 × 103 - 13 × 32 = 200 × 1000 - 13 × 9 = 200000 - 117 = 199883

Therefore, the change in the population of insects between day 0 and day 3 is:

199883 (day 3 population) - 200 (day 0 population) = 199683.

The insects' population increased by 199683 over the three-day period. This calculation assumes that the given expression accurately models the population growth without any restrictions like carrying capacity or environmental limitations that might typically affect population growth in nature.