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serious [3.7K]
3 years ago
6

Damian filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every ho

ur driven, and after driving for 3 hours, there were 6 gallons of gas left in the tank. Write an equation for the function G(t),G(t), representing the number of gallons of gas remaining in Damian's gas tank after tt hours of driving.
Mathematics
1 answer:
vesna_86 [32]3 years ago
7 0

Answer:

G(t)=12-2t

Step-by-step explanation:

Okay, first we need to find out how many gallons he lost, so we multiply 2 by 3 and get 6 gallons used.

Next, now knowing 6 gallons are left and 6 have been used we now add to get 12 gallons originally.

Then, now that we have the rate of change and the starting number we put together the equation to the way that best suits the question

Last, to check our work plug six into t next to the two and solve to get six gallons used,

I hope this helps you

If i am right a thanks would be appreciated if i am wrong please leave a comment

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So using points (6,71) and (2,y), and the slope of 15, plug them into the slope formula as such:

\frac{71-y}{6-2}=15

From here we can solve for y. Firstly, solve the subtraction:

\frac{71-y}{4}=15

Next, multiply both sides by 4:

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-y=-11

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4 years ago
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Answer:

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How would you answer this question?
grigory [225]

Answer: Choice B

If you lower your rates by 6% you will increase the number of occupancies by 12%

========================================================

Explanation:

Price Elasticity of Demand is found by dividing the percent change of demand over the percent change in price

\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}

If the price drops 6% leads to a 12% increase in demand, then we get this elasticity

\text{Price Elasticity of Demand} = \frac{\% \text{ change in demand}}{\% \text{ change in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\% \text{ increase in demand}}{6\% \text{ drop in price}}\\\\\text{Price Elasticity of Demand} = \frac{12\%}{-6\%}\\\\\text{Price Elasticity of Demand} = \frac{0.12}{-0.06}\\\\\text{Price Elasticity of Demand} = -2\\\\

The absolute value of that result is 2. We work backwards going from 2 to see the relationship between the 12% and 6%.

-------------

Side notes:

  • Choice A is incorrect as a price elasticity of demand larger than 2 means we have elastic (rather than inelastic) demand.
  • Choice C is incorrect because while raising rates does bring in more money in certain situations, there's a limit to how much the price goes up before people stop showing up. The prices can't go up forever. Also, the fact we have an elastic product means people are either forgoing this hotel or finding a substitute.
  • Choice D is incorrect. Products with high demand elasticity usually have substitutes. Any slight change in the price leads people to seek cheaper options. Unless we're dealing with a small town there are usually multiple hotels to choose from.
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