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20 Points Math Help Much Appreciated

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (5 points)

f(x) = 2149 ⋅ 0.9915x

A) Exponential growth function; -0.85%

B) Exponential growth function; 0.0085%

C) Exponential decay function; 0.0085%

D) Exponential decay function; -0.85%

Respuesta :

sqdancefan

Answer:

D) exponential decay, -0.85%

Step-by-step explanation:

The base of the exponential is less than 1, so the function is a decay function. As x increases, we multiply by a number smaller than 1 more times, so the function value keeps getting smaller and smaller.

The percentage change can be found by recognizing that the growth (decay) factor can be written as ...

... (1 + fraction of change)

So we have ...

... 0.9915 = 1 + (fraction of change)

Subtracting 1 gives ...

... -0.0085 = (fraction of change)

Expressing this as a percentage, we have ...

... (fraction of change) = -0.0085 × 100% = -0.85%

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