Question Video: Constructing Equivalent Exponential Functions with Different Bases from a Graph

Which of the following expressions does NOT describe the shown graph? [A] 𝑁 = 15 ⋅ (3/4)^−𝑡 [B] 𝑁 = 15 ⋅ 𝑒^0.288𝑡 [C] 𝑁 = 15 ⋅ 2^2.4𝑡 [D] 𝑁 = 15 ⋅ 2^(𝑡/2.4) [E] 𝑁 = 15 ⋅ (4/3)^𝑡

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Video Transcript

Which of the following expressions does not describe the shown graph?

At first, it may seem that the negative exponent would be the one that would be different from all of them. However, when you have a negative exponent, you can flip the fraction and the exponent will become positive. So it’s actually the same as E.

So a good place to start would be to plug in zero. And when we plug in zero into each of these for 𝑡, we get close to 20. So that didn’t help very much. So next if we plug in one for 𝑡, let’s see what we get. For A, we get exactly 20, so that works. For B, we get 20.006, still very close. But for C, we get something very large; it’s 79.17. So this will tell us that this will be our answer.

So comparing all of them, every single one except for C is multiplying a tiny number times 𝑡 if anything. However, C is multiplying 𝑡, the exponent, times a number. So it’s gonna grow much faster. Therefore, C would not describe the shown graph.