CHECK IF THE GIVEN FUNCTION IS EXPONENTIAL GROWTH OR DECAY

Tell whether the functions below show exponential growth or decay function.

Problem 1 :

y = (1/4)^x

Solution :

a = 1 and b = 1/4

0 < 1/4 < 1

So, it is exponential decay function.

Problem 2 :

y = 2^x

Solution :

a = 1 and b = 2

2 > 1

So, it is exponential growth function.

Problem 3 :

y = 1^x

Solution :

a = 1 and b = 1

Applying all real values of x, the value of y will stay same. It is not exponential or linear. So, it is neither.

Problem 4 :

y = 5^x

Solution :

a = 1 and b = 5

b = 5 > 1

So, the function is exponential growth function.

Problem 5 :

y = 0^x

Solution :

a = 1 and b = 0

So, the function is neither.

Problem 6 :

y = (2/3)^x

Solution :

a = 1 and b = 2/3

b = 2/3 < 1

So, the function is exponential decay function.

Problem 7 :

y = 9^x

Solution :

a = 1 and b = 9

b = 9 > 1

So, the function is exponential growth function.

Problem 8 :

y = (1/5)^x

Solution :

a = 1 and b = 1/5

b = 1/5 < 1

So, the function is exponential decay function.

Problem 9 :

y = 4^x

Solution :

a = 1 and b = 4

b = 4 > 1

So, the function is exponential growth function.

Problem 10 :

y = (5/6)^x

Solution :

a = 1 and b = 5/6

b = 5/6 < 1

So, the function is exponential decay function.