Eloise had to solve a system of inequalities that contained an exponential growth function and a linear function with positive slope.

She KNOWS that the two equations intersect at least once, and she was asked to state the interval where the linear exponential.

Which could be an answer to her system of inequalities?

Question

Eloise had to solve a system of inequalities that contained an exponential growth function and a linear function with positive slope.

She KNOWS that the two equations intersect at least once, and she was asked to state the interval where the linear > exponential.

Which could be an answer to her system of inequalities?

Mercury · Answer

choices

A) (-1, 3) 
B) (-1, [infinity]) 
C) (-[infinity], -1) 
D) (-[infinity], -1) ∪ (3, [infinity])

it is also stated that the linear graph and the exponential graph intersect at least once (could be once or twice)

considering the first situation (only one intersection), the linear graph is tangent to the exponential graph and will always be below the exponential gratph. therefore, the interval is empty (not one of the choices)

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so we have to consider the second situation (two intersections). notice how there is only a finite interval where the linear function is greater than the exponential function.

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from there, it should be clear which interval from the choices is actually possible for such a situation