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Elis [28]
1 year ago
12

1) Answer the following questions for the function y= 4^x

Mathematics
1 answer:
blondinia [14]1 year ago
7 0

a) Increasing function.

b) The growth factor is 4.

c) The asymptote is y tending to zero as x tends to negative infinity.

d) y = 1

c) The graph can be seen at the end.

<h3>What conclusions can we get about the given function?</h3>

Here we are given the following exponential function:

y =f(x) =  4^x

a) First, we want to know if the function is increasing or decreasing. Remember that a function is increasing if, as x increses, also does the value of y.

Here clearly we have an increasing function.

  • f(0) = 4^0 = 1
  • f(1) = 4^1 = 4
  • f(2) = 4^2 = 16

and so on...

b) Now we want to identify the growth factor. This is the number that is being exponentiated, so in:

y = 4^x

The growth factor is 4.

c) We have an asymptote as x tends to negative infinity, because we will eventually have denominator that tends to infinity, then we will have an asymptote that tends to zero, as x tends to negative infinity.

d) The y-intercept is what we get when we evaluate in x = 0, we have:

y = f(0) = 4^0 = 1

The y-intercept is y = 1.

e) The sketch of the exponential function can be seen in the image below.

If you want to learn more about exponential functions:

brainly.com/question/11464095

#SPJ1

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Ronisha invests $5000 in an account that earns 2.3% annual simple interest. After 3 years, Ronisha invests the interest earned i
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Very complicated problem, but thank goodness I have too much time and am a nerd.

Basically model 1st account as so.
Fv=pv(1+I)^N
Fv future value
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I interest
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So first equation is interest earned after 3 years
Y=5000(1+0.023)^3
Y=5353 (rounded up)
So we know that the interest earned is 5353-5000 which is 353.

Now Ronisha (clearly the name of a future investment genius) invests these 353$ in a new account.
Now remember we’re not solving for FV we’re cause we’re given that: 55.2$
However this is the interest earned not the future value. So if interest earned is fv - pv and we know pv
Fv - 353 = 55.2
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So now we reuse the formula
408.2 = 353(1+0.032)^x
Now just solve for x:
First divide both sides by 353
1.156 = 1.032^x
Remember the log rule that states x=b^y is same as y=logb(x)
So using the same logic:
X= log1.032(1.156)
Use some kind of calculator for that where you can adjust log base. But you basically get:
X= 4.602
So Ronisha has to basically invest 5 years or 4.6 years which is 4 years and 7 months.

Omg nevermind, wait it’s simple interest….
Sorry here’s the simple solution. My bad, but I worked so hard on the top part I don’t want to delete it.
I=prt
Interest = principal * rate * time
I= 5000(0.023)(3)=345
Then just do the same but plug 55.2 for I
55.2 = 345(0.032)t
Now solve for t
55.2 = 11.04t
t= 5

As you can see, similar logic where ultimately it takes 5 years. But this “genius” Ronisha should’ve just done compounding interest (my first calculation) and gotten it done in 4.6 years. Almost 5 months faster.
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simplify

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