Invasive species often experience exponential population growth when introduced into a new environment. Zebra mussels are an invasive species that have recently made their way into midwestern lakes. In about six months, a zebra mussel population quadruples in size. Suppose 10 zebra mussels are newly introduced into a local lake. Find a function Z(t) that models the population of zebra mussels t years after they have been introduced. Use the function to determine how many zebra mussels there will be in 15 months. Use the function to determine how many months will pass before the lake has one million zebra mussels.

The model for the population of zebra mussels

At 15 months, the population is 315.

The population of zebra mussels will reach 1,000,000 in 50 months.

Step-by-step explanation:

We can model this as:

Then, the model for the population of zebra mussels in time can be written as:

At 15 months, the population is:

The population at 15 months is Z=315.

Now, we have to calculate at which time the lake will have one million zebra mussels.

The population of zebra mussels will reach 1,000,000 in 50 months.

where are the images of the functions i can only see the question you typed.

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1