What is the yintercept of the exponential function? f(x)=−32(2)x−3+3
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Question
What is the yintercept of the exponential function? f(x)=−32(2)x−3+3
2 Answer

1. User Answers apologiabiology
I assume your equation is
[tex]f(x)=32(2)^{x3}+3[/tex]
x intercept is where the line crosses the x axis or where y=0
set y=f(x)=0 and solve
[tex]0=32(2)^{x3}+3[/tex]
minus 3 both sides
[tex]3=32(2)^{x3}[/tex]
divide both sides by 32
[tex] \frac{3}{32} =2^{x3}[/tex]
take the ln of both sides
[tex] ln(\frac{3}{32}) =(x3)ln(2)[/tex]
[tex] ln(\frac{3}{32}) =xln(2)3ln(2)[/tex]
add 3ln(2) to both sides
[tex] ln(\frac{3}{32})+3ln(2) =xln(2)[/tex]
divide both sides by ln(2)
[tex] \frac{ln(\frac{3}{32})+3ln(2)}{ln(2)} =x[/tex]
[tex] \frac{ln(\frac{3}{4})}{ln(2)} =x[/tex]
the x intercept is at [tex] x= \frac{ln(\frac{3}{32})+3ln(2)}{ln(2)} [/tex]
or aprox at x=0.415037 
2. User Answers facundo3141592
We want to get the yintercept of the given function, we will see that it is y = 7.
So we have the exponential function:
[tex]y = f(x) = 32*(2)^{x  3} + 3[/tex]
We want to get the yintercept, it is just given by evaluating the function in x = 0, by doing that, we will get:
[tex]y = f(0) = 32*(2)^{0  3} + 3 = 7[/tex]
So the yintercept of the given function is y = 7.
If you want to learn more about function's intercepts, you can read:
https://brainly.com/question/1354826