Below are a variety of distances. Move each reasonable distance for Miguel to travel in a day to the reasonable category and move an unreasonable distance to the unreasonable category.For a solution to be reasonable, it must make sense. In this section, you are going to interpret and decide whether or not the solution is reasonable. You can practice what is reasonable and unreasonable below.
Miguel is leaving for his vacation today. Before he leaves for the airport, he goes for a morning walk. After packing, he then drives his car to the airport where he flies to his destination.
Below are a variety of distances. Move each reasonable distance for Miguel to travel in a day to the reasonable category and move an unreasonable distance to the unreasonable category.
You may have already used reasonableness when taking a multiple choice test. If not, you can practice a test taking skill. Below are some multiple choice test questions.
Without actually solving the problem, select a reasonable solution. Click on the unreasonable solutions for reasons why they are unreasonable.
If you didn’t review the unreasonable answers, please make sure that you do so now. They provide information that will assist you in finding a reasonable solution.
This is a great testing strategy. Eliminate the answers that you know are not reasonable, and then focus on the remaining answers to find the correct one.
Interactive popup. Assistance may be required.
No, x = 2.231 is not a reasonable answer, because 42 = 16 and 43 = 64. In order to be equal to 60, x has to be closer to 3 than 2.
f(x) = 2 over 3 2x 3 , x = 2.1
Interactive popup. Assistance may be required.
Choices A and D are unreasonable, because the answer isn’t negative. The negative exponent means the solution it is the reciprocal.
Interactive popup. Assistance may be required.
Start with something you know. You know 32 is close to 32.1 and 32 = 9. Also, 2.1 is close to 2 and you know 22 = 4. C is a reasonable solution since it is close to the values you found.
The number of cattle ranches in Texas (in thousands) can be represented by the equation R(t) = 120(0.887t) where t is the number of years since 1980.
Interactive popup. Assistance may be required.
The number of cattle ranches is decreasing. In previous lessons, you learned that since 0.887 is less than 1, it is decreasing.
Interactive popup. Assistance may be required.
Solving the equation algebraically, R(50) = 120(0.88750) = 0.299. Remember, this is in thousands, so there would be more than 100 ranches. The reasonableness of this solution may not be accurate because the equation represents the trend for cattle ranches in 1980, which could have changed by the year 2030.
Interactive popup. Assistance may be required.
Exponential and logarithmic equations are inverses of each other.
In the activity below, practice selecting a reasonable answer by matching the equation with a reasonable solution.