The equation for the graph is y = [tex]2(3)^{x} -5[/tex] .
What are Exponential Equations?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
Standard exponential equation :
y = [tex]a(b)^{x} + k[/tex]
where a is the initial value
b represents the base of the exponential function
x will represent the input of the function
y = k is the single horizontal asymptote
k is constant
According to the question
The figure in the graph is an exponential graph .
To derive the equation
we will use Standard exponential equation :
y = [tex]a(b)^{x} + k[/tex]
Now,
There are two points in graph
(0.-3) and (1,1)
k = - 5 ( distance from 0)
now ,
Substituting the values
y = [tex]a(b)^{x} + k[/tex]
y = [tex]a(b)^{x} -5[/tex]
for point (0.-3)
-3 = [tex]a(b)^{0} -5[/tex]
-3 = [tex]a -5[/tex]
a = 2
for point (1,1)
1 = [tex]2(b)^{1} -5[/tex]
1 = 2b - 5
b = 3
Therefore , equation of exponential graph is
y = [tex]2(3)^{x} -5[/tex]
Hence ,The equation for the graph is y = [tex]2(3)^{x} -5[/tex] .
To know more about Exponential Equations here:
https://brainly.com/question/23729449
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