Short Answer D The first thing that must be done is to see what e raised to a minus number does. Try a real simple example
y = 5e^-0.05 Put that into your calculator. You get 5 * e ^ - 0.05 =
The result is getting smaller. The answer I get is 4.7 which is less than 5. That means that our insect population is going to go down. What will happen if you change that -0.05 to a plus 0.05 Try it again.
5*e^0.05 = I get 5.25 The number is increasing 5.25 > 5.
What have you done? You have just eliminated two possible answers. a and c will both make 26 go up. You don't want either of them.
So now we need to look at B and D B won't work. Remember that t is a number in years. Any other number represents millions of insects. So the second equation must be written as P>2 The population must be kept at 2 million insects. Until then the first equation decreases the insect's numbers.
An exponential function with a positive exponent means function increases with time t. An exponential function with a negative exponent means function decreases with time t. So we're looking for a function with a NEGATIVE exponent.
Also, since question says population will remain CONSTANT at the minimum of 2 (millions) insects, so it should not be a function of time t. Therefore this condition should be written as P>=2 (millions) [and not 2t].
Given the above information, it will be up to you to choose the correct answer choice.
