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Consider the following relationships:A: 𝑦=𝑥4B: 𝑦=𝑥−4C: 𝑦=34𝑥D: 𝑦=3−4𝑥1. Which of these is an example of an exponential decay relationship and which is an example of an exponential growth relationship?

Question

Consider the following relationships:A: 𝑦=𝑥4B: 𝑦=𝑥−4C: 𝑦=34𝑥D: 𝑦=3−4𝑥1. Which of these is an example of an exponential decay relationship and which is an example of an exponential growth relationship?

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Solution

An exponential growth relationship is one where the value of y increases as x increases, while an exponential decay relationship is one where the value of y decreases as x increases.

A: 𝑦=𝑥^4 is an example of an exponential growth relationship. As x increases, the value of y (which is x to the power of 4) also increases.

B: 𝑦=𝑥−4 is neither an exponential growth nor decay relationship. It's a linear relationship because the exponent on x is 1.

C: 𝑦=34𝑥 is also not an exponential relationship. It's a linear relationship because the exponent on x is 1.

D: 𝑦=3−4𝑥 is an example of an exponential decay relationship. As x increases, the value of y (which is 3 minus 4 times x) decreases. However, it should be noted that this is not a standard form of an exponential decay function. A standard form would look like y=a*(b^x), where 0<b<1.

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