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Given the Exponential Equation, determine the Initial Value and Rate of Change as a Percent for each of the following.

Given The Exponential Equation Determine The Initial Value And Rate Of Change As A Percent For Each Of The Following class=

Sagot :

The formula for calculating exponential growth is expressed as

y = a(1 + r)^n

where

a is the initial value

y is the final value

n is the time

r is the growth rate

The formula for calculating exponential decay is expressed as

y = a(1 - r)^n

For y = 1010(1.05)^x,

initial value = 1010

1 + r = 1.05

r = 1.05 - 1 = 0.05

Since it is positive, it is exponential growth

Growth percent = 0.05 x 100 = 5%

For y = 4932(1.26)^x,

initial value = 4932

1 + r = 1.26

r = 1.26 - 1 = 0.26

Growth percent = 0.26 x 100 = 26%

For y = 2835(1.065)^x,

initial value = 2835

1 + r = 1.065

r = 1.065 - 1 = 0.065

Since it is positive, it is exponential growth

Growth percent = 0.065 x 100 = 6.5%

For y = (0.96)^t,

initial value = 1

1 - r = 0.96

r = 1 - 0.96 = 0.04

decay percent = 0.04 x 100 = 4%

For y = 4660(0.89)^x,

initial value = 4660

1 - r = 0.89

r = 1 - 0.89 = 0.11

decay percent = 0.11 x 100 = 11%

For y = 3078(1.09)^t,

initial value =3078

1 + r = 1.09

r = 1.09 - 1 = 0.09

Growth percent = 0.09 x 100 = 9%

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