# CHECK IF THE GIVEN FUNCTION IS EXPONENTIAL GROWTH OR DECAY

Exponential function :

If the growth or decay involves using multiplication, then it should be a exponential function.

y = a(b)x

a is starting value

If b > 0 for growth and 0 < b < 1 when it is 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 = 2x

Solution :

a = 1 and b = 2

2 > 1

So, it is exponential growth function.

Problem 3 :

y = 1x

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 = 5x

Solution :

a = 1 and b = 5

b = 5 > 1

So, the function is exponential growth function.

Problem 5 :

y = 0x

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 = 9x

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 = 4x

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.

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