The exponential function ggg, whose graph is given below, can be written as g(x)=a\cdot b^xg(x)=a⋅b
x
g, left parenthesis, x, right parenthesis, equals, a, dot, b, start superscript, x, end superscript.
Complete the equation for g(x)g(x)g, left parenthesis, x, right parenthesis.
Answers
Given:
The exponential function g, whose graph is given below, can be written as g(x)=a\cdot b^x.
To find:
Complete the equation for g(x)
Solution:
Consider the attached graph while going through the following steps.
From given, we have,
g (x) = a · b^x
when x = 0, we have, g (x) = 4
g (0) = a · b^0 = 4
g (0) = a · 1 = 4
⇒ g (0) = a = 4
∴ a = 4
similarly, when x = 1, we have, g (x) = 2
g (1) = a · b^1 = 2
g (1) = a · b = 2
⇒ g (1) = a · b
g (1) = 4 · b = 2
∴ b = 1/2
Therefore, a is an independent term.
Whereas, b is a dependent variable and changes with the value of x.
The complete function depends on the product of a constant value "a" and a dependent variable "b".
∴ g (x) = 4 · (1/2)^x is the required equation for g(x)
Answer:
g(x)=8* (1/4)^x
Step-by-step explanation:
In the exponential form of a*b^x
A is the value of the function when X=0
B is the constant ratio of g(x) for consecutive integer values of X
The Y-intercept of the graph is (0,8), so A=8
The graph also passes through the point (1,2), because ) and one are consecutive integer x- values, we can calculate the common ratio.
b=2/8
=1/4
The equation for g(x) is
g(x)=8*(1/4)^x