Answer:
x = 6
Step-by-step explanation:
As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.
For small values of x, we have that f(x) < g(x). For example:
f(1) = 1/2 * 2 = 1
g(1) = 5*1 + 2 = 7
f(2) = 1/2 * 4 = 2
g(2) = 5*2 + 4 = 14
So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.
For x = 5, we have:
f(5) = 1/2 * 32 = 16
g(5) = 5*5 + 4 = 29
For x = 6, we have:
f(6) = 1/2 * 64 = 32
g(6) = 5*6 + 4 = 34
For x = 7, we have:
f(7) = 1/2 * 128 = 64
g(7) = 5*7 + 4 = 39
So the largest integer value of x for f(x) ≤ g(x) is x = 6.
Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).
Answer:
<em>c</em>
Step-by-step explanation:
I say c because i couldn't decide between c or d.
Answer:
because of his big work that hes doing and because he earns it
Step-by-step explanation:
Answer:
The ira will contain $228,278.05 when he retires at age 65. This is 6.04 times the amount of money he deposited.
Step-by-step explanation:
In order to solve this problem, we can make use of the following formula:
![FV=PMT[\frac{(1+i)^{n}-1}{i}]](https://tex.z-dn.net/?f=FV%3DPMT%5B%5Cfrac%7B%281%2Bi%29%5E%7Bn%7D-1%7D%7Bi%7D%5D)
Where:
FV= Future value of the ira
PMT= the amount of money you deposit each month
i= is the interest rate per period
n=number of periods
in this case we will assume the interest will be compounded each month.
So:
FV this is what we need to know.
PMT= $75 the amount he will deposit each month
t = 42 years,
this is 65-23=42
n=42 years * 12 months/year = 504 months
i=0.07/12
So we can now use the given formula:
![FV=75[\frac{(1+\frac{0.07}{12})^{504}-1}{\frac{0.07}{12}}]](https://tex.z-dn.net/?f=FV%3D75%5B%5Cfrac%7B%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B504%7D-1%7D%7B%5Cfrac%7B0.07%7D%7B12%7D%7D%5D)
So we get:
FV=$228,278.05
which is the amount of money he will have after 42 years.
In total, he deposited:
$75*504months = $37,800
so he will have:
times the amount of money he deposited throughout this time.
Answer:
0
Step-by-step explanation:
the opposite is 1 -7/8 when you add them together they cancel out to zero
