Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements:

1. As x increases infinitely, the y-values are continually doubled for each single increase in x.
2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.

She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine’s statements and her conclusion?

Statement 1 is incorrect because the y-values are increased by 2, not doubled.

Statement 2 is incorrect because the y-values are doubled, not halved.

The conclusion is incorrect because the range is limited to the set of integers.

The conclusion is incorrect because the range is limited to the set of positive real numbers.

Find the greatest common factor of the followig monomials 21u^5v,3u^4v^6, and 3u^2v^5

Which expression is rational? 6. , square root two, square root 14, square root 49

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.