Question

question 2.1
a power company offers customers both natural gas and electricity. the following functions help calculate the monthly cost for each service

• electricity: ( e(k)=0.13k + 20 ) models the monthly cost of electricity, in dollars, where ( k ) is the number of kilowatt - hours used
• natural gas: ( g(t)=1.63t + 10 ) models the monthly cost of natural gas, in dollars, where ( t ) is the number of therms used

for a customer who uses both electricity and natural gas, what will be the total monthly cost for using 500 kilowatt - hours and 30 therms?
$88.90
$85.90
$113.90
$143.90

Explanation:

Step1: Calculate the cost of electricity

Substitute \(k = 500\) into \(E(k)=0.13k + 20\).
\(E(500)=0.13\times500+20\)
\(E(500)=65 + 20=85\)

Step2: Calculate the cost of natural gas

Substitute \(T = 30\) into \(G(T)=1.63T + 10\).
\(G(30)=1.63\times30+10\)
\(G(30)=48.9+10 = 58.9\)

Step3: Calculate the total cost

Add the cost of electricity and natural gas.
\(Total=E(500)+G(30)=85 + 58.9=143.9\)

Answer:

\(\$143.90\)