Let's break down the problem step-by-step to find the value of [tex]\( E \)[/tex] when [tex]\( q = 3000 \)[/tex] and then round it to the nearest cent.
1. Identify the given equation and the values:
The equation is:
[tex]\[
E = 5.16q + 23000
\][/tex]
Given that [tex]\( q = 3000 \)[/tex], we are to find the value of [tex]\( E \)[/tex] for this quantity of kits.
2. Substitute the value of [tex]\( q \)[/tex] into the equation:
[tex]\[
E = 5.16 \cdot 3000 + 23000
\][/tex]
3. Perform the multiplication first:
[tex]\[
5.16 \cdot 3000 = 15480
\][/tex]
4. Add the result to 23000:
[tex]\[
E = 15480 + 23000 = 38480
\][/tex]
5. Round the result to the nearest cent:
In this case, we have calculated:
[tex]\[
E = 38480.00
\][/tex]
Since the result [tex]\( 38480 \)[/tex] already has no fractional cents, rounding to the nearest cent does not change the value.
So, the final values are:
- The value of [tex]\( E \)[/tex] before rounding: [tex]\( 38480.00 \)[/tex]
- The value of [tex]\( E \)[/tex] after rounding to the nearest cent: [tex]\( 38480.00 \)[/tex]
Thus, the calculated energy cost [tex]\( E \)[/tex] for 3000 kits is \$38,480.00 when rounded to the nearest cent.
