Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 96(1.03)



Answer :

Answer:

  • Growth; 3%

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According to the function the change is 1.03.

It can be shown as:

  • 1.03 = 103% = 100% + 3%

As we see it is a 3% growth.

After calculating, the percentage increase will be equal to 3%.

What is the Percentage?

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the data mentioned in the question,

In the form of the exponential equation.

y = [tex]ab^x[/tex]

The initial value is a, b is the growing (or decay) factor, and (b - 1) × 100% is the growth (or decay) rate,

A further point is that the equation depicts growth if b > 1 and decay if b < 1.

Taking into consideration the aforementioned, we discover that for exponential function,

y = 96(1.03)

a. Since 1.03 > 1, this show the growth in relationship.

b. the value of b = 1.03, so the growth factor is 1.03

c. The rate of growth

= ( 1.03 -1 ) × 100%

= 0.03 × 100% = 3%

d. Since 'a' has a value of 96, the starting value is also 96.

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