HOW TO DETERMINE EXPONENTIAL GROWTH OR DECAY WITHOUT GRAPHING

Problem 1 :

y = 1200 ⋅ (1 + 0.3)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 1200 ⋅ (1 + 0.3)^t

Exponential growth :

A = P (1 + r)^t

So, the function represents exponential growth.

B. To find initial value :

Initial value P = 1200

C.  Rate of growth :

r = 0.3

Problem 2 :

y = 55 ⋅ (1 - 0.02)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 55 ⋅ (1 - 0.02)^t

Exponential decay :

A = P (1 - r)^t

So, the function represents exponential decay.

B. To find initial value :

Initial value P = 55

C.  Rate of growth :

r = 0.02

Problem 3 :

y = 100 ⋅ (1.25)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 100 ⋅ (1.25)^t

y = 100 ⋅ (1 + 0.25)^t

Exponential growth :

A = P (1 + r)^t

So, the function represents exponential growth.

B. To find initial value :

Initial value P = 100

C.  Rate of growth :

r = 0.25

Problem 4 :

y = 5575 ⋅ (0.65)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 5575 ⋅ (0.65)^t

y = 5575 ⋅ (1 - 0.35)

Exponential decay :

A = P (1 - r)^t

So, the function represents exponential decay.

B. To find initial value :

Initial value P = 5575

C.  Rate of decay :

r = 0.35

Problem 5 :

y = 2000 ⋅ (1.05)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 2000 ⋅ (1.05)^t

y = 2000 ⋅ (1 + 0.05)^t

Exponential growth :

A = P (1 + r)^t

So, the function represents exponential growth.

B. To find initial value :

Initial value P = 2000

C.  Rate of growth :

r = 0.05

Problem 6 :

y = 14000 ⋅ (0.92)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 14000 ⋅ (0.92)^t

y = 14000 ⋅ (1 - 0.08)^t

Exponential decay :

A = P (1 - r)^t

So, the function represents exponential decay.

B. To find initial value :

Initial value P = 14000

C.  Rate of decay :

r = 0.08

Problem 7 :

y = 2250 ⋅ (1 - 0.9)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 2250 ⋅ (1 - 0.9)^t

Exponential decay :

A = P (1 - r)^t

So, the function represents exponential decay.

B. To find initial value :

Initial value P = 2250

C.  Rate of growth :

r = 0.9

Problem 8 :

y = 10 ⋅ (1 + 0.04)^t

A. Does this function represent exponential growth or exponential decay ?

B. What is your initial value ?

C. What is the rate of growth or rate of decay ?

Solution :

A. 

Given function is y = 10 ⋅ (1 + 0.04)^t

Exponential growth :

A = P (1 + r)^t

So, the function represents exponential growth.

B. To find initial value :

Initial value P = 10

C.  Rate of growth :

r = 0.04