HOW TO FIND PERCENT CHANGE OF AN EXPONENTIAL FUNCTION

Determine growth/ decay, the percent of change, and initial value.

Problem 1 :

7500(1 + 0.03)^x

Solution :

7500(1 + 0.03)^x

Initial value = 7500 and it is exponential growth function.

Comparing the given function with y = a(1 士 r)^x

we get r = 0.03

To convert the decimal as percentage, we have to multiply by 100%.

0.03 x 100%

= 3%

So, the required percentage change is 3%.

Problem 2 :

(0.85)^x

Solution :

(0.85)^x

Initial value = 1

Comparing the given function with y = a(1 士 r)^x

(0.85)^x = (1 - 0.15)^x

r = 0.15

Exponential decay function.

Converting it as percentage :

= 0.15 x 100%

= 15%

So, the required percentage change is 15%.

Problem 3 :

900(1.27)^x

Solution :

900(1.27)^x

Initial value = 900

Comparing the given function with y = a(1 士 r)^x

900(1.27)^x = 900 (1 + 0.27)^x

r = 0.27

Exponential growth function.

Converting it as percentage :

= 0.27 x 100%

= 27%

So, the required percentage change is 27%.

Problem 4 :

24000(1 - 0.08)^t

Solution :

24000(1 - 0.08)^t

Initial value = 24000

Exponential decay functions.

Comparing the given function with y = a(1 士 r)^x

r = 0.08

Converting into percentage,

= 0.08 x 100%

= 80%

So, the required percentage change is 80%.

Problem 5 :

750(1.15)^t

Solution :

= 750(1.15)^t

= 750(1 + 0.15)^t

Initial value = 750

Exponential growth function.

Comparing the given function with y = a(1 士 r)^x

r = 0.15

Converting into percentage,

= 0.15 x 100%

= 15%

So, the required percentage change is 15%.

Problem 6 :

250000(0.65)^t

Solution :

= 250000(0.65)^t

= 250000(1 - 0.35)^t

Initial value = 250000

Exponential decay function.

Comparing the given function with y = a(1 士 r)^x

r = 0.35

Converting into percentage,

= 0.35 x 100%

= 35%

So, the required percentage change is 35%.