first you top off your gas tank in olympia. you then drive your hummer to spokane, traveling 319.4 miles. you fill up your gas tank with 28.68 gallons of premium gasoline that costs $2.89 per gallon. what is your gas mileage in miles per gallon and how much does it cost to drive just one mile in your hummer (unit rate of cost per mile)?

Step-by-step explanation:

The distance that you travelled in your hummer between Olympia and Spokane is 319.4 miles.

You fill up your gas tank with 28.68 gallons of premium gasoline that costs $2.89 per gallon. This means that the total cost of premium gasoline that you bought would be

2.89 × 28.68 = $82.8852

your gas mileage in miles per gallon is 319.4/28.68 = 11.14 miles per gallon.

Therefore, if it costs $82.8852 to drive 319.4 miles,

then the cost of just one mile in your hummer would be

82.8852/319.4 = $0.26 per mile.

$649.60

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: