The number of people who vote early doubles every week leading up to an election. This week 1200 people voted early. The expression 1200 (multiplied by) 2^w models the number of people who will vote early w weeks after this week. Evaluate the expression for w= -3. Describe what the value of the expression represents in the situation.

2^-3=1/8

It looks like the vote three weeks earlier.

1200*1/8=150

To evaluate the expression 1200 multiplied by 2^w when w = -3, we substitute -3 into the expression:

1200 * 2^(-3)

To simplify this expression, recall that any number raised to the power of -n is equal to 1 divided by that number raised to the power of n. Applying this rule:

1200 * (1 / 2^3)

1200 * (1 / 8)

1200 / 8

150

The value of the expression for w = -3 is 150. In this situation, the expression represents the number of people who voted early three weeks before the current week. Therefore, 150 people voted early three weeks before this week.

To evaluate the expression 1200 multiplied by 2^w for w = -3, we need to substitute the value of w into the expression and simplify.

Given the expression 1200 * 2^w, when we substitute w = -3, we get:
1200 * 2^-3

To simplify this expression, we can rewrite 2^-3 as 1/2^3.

1200 * (1/2^3)

Simplifying further, we can evaluate 1/2^3 as 1/8:

1200 * 1/8

Multiplying 1200 by 1/8 gives us:

1200/8 = 150

So, when w = -3, the expression 1200 * 2^w evaluates to 150.

In the given situation, the value of the expression represents the estimated number of people who voted early three weeks before the current week. In this case, it indicates that 150 people voted early three weeks ago.