Question

HELP PLS THANKS......The National Science Organization is monitoring the continuous exponential decline of an insect species due to deforestation. They do not know exactly how many there are remaining, but the model they are using represents the minimum number remaining in the world. They are putting measures into place in order to avoid extinction which will take effect when the minimum number reaches a certain point.

According to the model, the minimum number of the species remaining, in millions, is constantly decreasing at a rate of 7.9% each year. There are at least 26 million of the species in the world right now. Once the minimum population reaches 2 million, the measures will be instated which should stop the decrease and keep the minimum population at 2 million.

If P represents the actual population of the insects in the world, in millions, and t represents the time in years, then which of the following systems of inequalities can be used to determine the possible number of insects in the world over time?
OPTIONS BELOW:

Answer 1

The answer is the last answer choice

Answer 2

It is given that the decay is exponential. It is also given that the decrease is constant at a rate of 7.9% per year. This can be rewritten as

`(7.9)/(100)=0.079`

Now, we know that right now there are atleast 26 million of the species. Thus, the starting or the initial amount of the decay is 26.

Therefore, this part of the inequality will be:
`P\geq26e^(-0.079t)`, where the minus sign before the 0.079 denotes the decay.

Also, we know that the population cannot go below 2 million. Therefore, we will have:
`P\geq2`.

Combining the above two we get:

`P\geq26e^(-0.079t)`, and

`P\geq2`

Thus, out of the given options, the last option is the correct option.