Given function: [tex]g(x)=-5^{x+3}+7[/tex]
We need to find the correct graph in the given options.
In order to find the correct, we need to find the x-intercept.
In order to find the x-intercept, we need to put given function equal to 0 and then solve for x.
[tex]-5^{x+3}+7=0[/tex]
Subtracting 7 from both sides, we get
[tex]-5^{x+3} = -7[/tex]
Dividing both sides by -1, we get
[tex]5^{x+3} =7[/tex]
Taking ln on both sides, we get
[tex]ln(5^{x+3}) = ln(7)[/tex]
(x+3) [tex]ln(5) = ln(7)[/tex]
Dividing both sides, by ln(5), we get
[tex]x+3=\frac{ln(7)}{ln(5)}[/tex]
x+3 =1.21
x= 1.21 -3
x=-1.79.
From the given options, we can see the 4th option has x-intercept at -1.79.
Therefore, 4th option is correct option.
