Question

the function y= 11,600(1/4)^x represents exponential (growth or decay) rewriting the base in terms of the rate of growth or decay results in the function y= 11,600(___)^x in this function r= ___ which indicates that the value of y (increases or decreases) by ___% each time.

Answer 1

Answers:

• decay
• 1-0.75
• -0.75
• decreases
• 75%

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Step-by-step explanation:

An exponential function has the template

y = a*b^x

where,

• a = starting value
• b = growth or decay factor

We have b = 1/4 = 0.25 as the base of the exponent.

Since 0 < b < 1 is the case, we have exponential decay

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We can also have this template

y = a*(1+r)^x

I replaced b with 1+r

If we set this equal to 0.25 and solve for r, we get:

1+r = 0.25

r = 0.25-1

r = -0.75

The negative r value is another way to see how we have exponential decay

So we go from 1+r to 1+(-0.75) aka 1-0.75 as the base of the exponential.

In other words, 11600(0.25)^x is the same as 11600(1-0.75)^x

In the second format, it's much easier to see what the r value is.

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The r value r = -0.75 converts to the percentage 75%

It means y decreases by 75% each time x goes up by 1.