9122005

Mth163

I would Just like to know if i am doing the following problem right. The question states Obtain expressions for the following: Where value(t)=$1000(1.07)^t find for value(t+3) and value(t+3)/value of(t)When I did these problems I came out with $1000(1.07)^(t+3) and $1000(1.07)^(t+3)/$1000(1.07)^t Am I anywhere near to being correct?

Good but that expression can be simplified. The following was also posted with questions for 050914:

value(t+3) / value(t) = 1000(1.07)^(t+3)/(1000 * 1.07^t).

This can be simplified.

Recall that a^(b + c) = a^b * a^c. So

$1000 ( 1.07)^(t + 3) = $1000 ( 1.07)^t * (1.07)^3.

So

1000(1.07)^(t+3)/(1000 * 1.07^t) = $1000 ( 1.07)^t * (1.07)^3 / ( $1000 * 1.07^t) = 1.07^3.

Obtain expressions for the following: Where illumination(distance)=50/distance^2 for illumination(distance)/illumiation(2*distance). The answer I got is (50/distance)/(50/4distance^2)Is this correct?

Also good, but be careful of your grouping. Your expression at this point should read

(50/distance)/(50/ (4distance^2) ).

(50/4distance^2) means 50 / 4 * distance^2, or 50 distance^2 / 4, by order of operations; and that would not be right.

This is also posted under Questions for 050914:

There are two expressions in the expression illumination (distance)/illumination(2*distance).

One is

illumintation(distance)

and the other is

illumination (2 * distance).

You are given that

illumination (distance) = 50 / distance^2.

From this it follows that

illumination (2 * distance) = 50 / (2 * distance)^2.

So

illumination (distance)/illumination(2*distance) = ( 50 / distance^2 ) / (50 / (2 * distance)^2 ).

(a / b) / ( c / d) = (a / b) * ( d / c), so

( 50 / distance^2 ) / (50 / (2 * distance)^2 ) = ( 50 / distance^2 ) * (2 * distance)^2 / 50.

50 / 50 = 1 so the expression is

(2 * distance)^2 / distance^2, which is equal to

2^2 * distance^2 / distance^2. Since distance^2 / distance^2 = 1, the final result is just

2^2, or 4.