# Math Help - Exponential functions

1. ## Exponential functions

For the function: y = 3(2)^x - 1
Are these correct?
Domain: -infinity to infinity
Range: -1 to infinity
Y-Asymptote: -1

I also need to find the intervals of increase/decrease but I am unsure on how to do that.

And my last question. How do you find the growth rate of 10000(1.06)^x

2. Originally Posted by olen12
For the function: y = 3(2)^x - 1
Are these correct?
Domain: -infinity to infinity
Range: -1 to infinity
Y-Asymptote: -1

I also need to find the intervals of increase/decrease but I am unsure on how to do that.
All of this is correct although with your range you don't include -1 itself. The range should be written as $y \in (-1,\infty)$

Originally Posted by olen12

I also need to find the intervals of increase/decrease but I am unsure on how to do that.
I think you mean

as $x \rightarrow \infty, y \rightarrow \infty$

as $x \rightarrow -\infty, y \rightarrow -1$

Originally Posted by olen12

And my last question. How do you find the growth rate of 10000(1.06)^x
As the exponent has base 1.06 then the growth rate is 6% with an initial value of 10,000

Hope that helps!

3. Originally Posted by olen12
For the function: y = 3(2)^x - 1
Are these correct?
Domain: -infinity to infinity
Range: -1 to infinity
Y-Asymptote: -1

I also need to find the intervals of increase/decrease but I am unsure on how to do that.

And my last question. How do you find the growth rate of 10000(1.06)^x
The range is $-1 \leq y \leq \infty$ because as you said before there is an asymptote at -1. Otherwise correct.

The interval of increase or decrease depends on what the value of x is.

You can find the growth rate by using the binomial expansion (1.06 = 1+0.06) or by plugging in x or using logarithms depending on what you know