Question

The number of wild sheep on a mountain can be modeled with an exponential function. In the first count, there are

640 sheep. One year later, there are 576. This trend continues for six years. What is a reasonable estimate for the
number of sheep six years after the first count.
320 sheep
340 sheep
378 sheep
384 sheep

Answer 1

340 sheep.

Explanation:

There is a decrease of 640 - 576 = 64 sheep in the first year.

This is 1/10 of the previous year, so the number in year 2 is 0.90 of the number of sheep in year 1, so a model for this could be:

640(0.90)^x where x is the year.

So after 6 years the estimate would be 640 *(0.90)^6

= 340 sheep.