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 = 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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM