Electricity Usage in Electric Cars

The video tutorial explains how an electric car uses electricity, modeled by the function e(m), where m is the miles traveled. It starts with 85 kilowatt hours and calculates the electricity left after driving five miles. The process involves graphing e(m), understanding the area under the curve, and using integration to find the electricity used. The tutorial applies the power rule of integration to determine the antiderivative and calculates the remaining electricity, rounding to the nearest tenth. The final result is 83.5 kilowatt hours left after five miles.

What does the function e(m) represent in the context of electric cars?

• The speed of the car in miles per hour

• The cost of electricity per mile

• The amount of electricity used per mile

• The total distance traveled by the car

On the graph of e(m), what does the horizontal axis represent?

• Electricity usage rate

• Time in hours

• Distance in miles

• Cost in dollars

What does the area under the curve of e(m) and the x-axis represent?

• The cost of electricity

• The total distance traveled

• The average speed of the car

• The total electricity used

Why is a definite integral used in this context?

• To calculate the total distance traveled

• To find the average speed of the car

• To determine the electricity used over a specific distance

• To estimate the cost of electricity

What is the expression for e(m) used in the integral?

• Negative 0.5 times m

• 0.5 times the square root of m

• Negative 0.13 times the square root of m plus 0.5

• 0.13 times m squared

What is the first step in applying the power rule of integration to e(m)?

• Multiply by the derivative of m

• Add one to the exponent of m

• Subtract one from the exponent of m

• Divide by the original exponent of m

How is the expression 'negative 0.13' simplified in the integration process?

• As negative 13 one-hundredths

• As negative 0.013

• As negative 1.3

• As negative 130

What is the final step in determining the remaining electricity after five miles?

• Adding the initial electricity to the integral result

• Subtracting the integral result from the initial electricity

• Multiplying the integral result by the initial electricity

• Dividing the initial electricity by the integral result

What is the approximate amount of electricity used after five miles, rounded to the tenths place?

• 1.5 kilowatt hours

• 2.0 kilowatt hours

• 1.0 kilowatt hours

• 2.5 kilowatt hours

How much electricity is left in the battery after driving five miles?

• 82.0 kilowatt hours

• 85.0 kilowatt hours

• 83.5 kilowatt hours

• 80.0 kilowatt hours