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.

step-by-step explanation:

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