Question

A population of cattle is increasing at a rate of 300+30t per year, where t is measured in years. By how much does the population increase between years 7 and 11 ?

Answer 1

The population of cattle will increase by 2850 between years 7 and 11, as calculated by summing the increase for each year using the given formula.

Step-by-step explanation:

The student asked how much the population of cattle would increase between years 7 and 11, given it's increasing at a rate described by the formula 300+30t per year, with t representing the number of years. To find the total increase over that period, you must calculate the rate for each individual year and then sum them.

For year 7: 300 + (30 × 7) = 300 + 210 = 510
For year 8: 300 + (30 × 8) = 300 + 240 = 540
For year 9: 300 + (30 × 9) = 300 + 270 = 570
For year 10: 300 + (30 × 10) = 300 + 300 = 600
For year 11: 300 + (30 × 11) = 300 + 330 = 630

The total increase from year 7 to year 11 is the sum of each year's population increase:

510 + 540 + 570 + 600 + 630 = 2850

Therefore, the total increase in population between years 7 and 11 is 2850 cattle.