You must get by itself so you must add to both side which results in

.

You must get the square root of both side to undue the exponent.

This leaves you with .

But since you square the in the equation, the original value you plug can also be its negative value since squaring it will make it positive anyway.

This means your answer can be or .

Rewrite the right side as base 2.

Replace the term into the equation.

With similar bases, we can set the exponents equal.

Subtract six from both sides.

Divide by negative three on both sides.

The answer is:

a)

This is exponential decay since the base, , is between and .

b)

This is exponential growth since the base, , is greater than .

For , our base is greater than so we have exponential growth, meaning the function is increasing. Also, when , we know that since . The only graph that fits these conditions is .

For , we have exponential growth again but when , . This is shown on graph .

For , we have exponential decay so the graph must be decreasing. Also, when , . This is shown on graph .

Because both sides of the equation have the same base, set the terms equal to each other.

Add 9 to both sides:

Then, subtract 2x from both sides:

Finally, divide both sides by 3:

The -intercept of any graph describes the -value of the point on the graph with a -value of .

Thus, to find the -intercept substitute .

In this case, you will get,

.

Both 27 and 9 are powers of 3, therefore the equation can be rewritten as

.

Using the Distributive Property,

.

Now that both sides have the same base, set the two exponenents equal and solve.

Add 12 to both sides:

Subtract from both sides:

We need to determine the constants and . Since in 2010 (when ), then and

To get , we find that when , . Then .

Using a calculator, , so .

Then our model equation for the fish population is

Let's convert to base .

We know the following:

Simplify.

Solve.

The -intercept of any function describes the point where .

Substituting this in to our funciton, we get: