Answer:
see below
Step-by-step explanation:
The problem statement seems to presume you have seen an exponential function like this written as ...
f(t) = a0·(1 +r)^t
where a0 is the value corresponding to f(0) and "r" is the fractional rate at which the value increases for each increment of t.
Here, 1+r corresponds to 1.04 in the given function, so r = 0.04 = 4%. When the value is <em>greater than 0</em>, it means there is an <em>increase</em> by that fraction each time t increases by 1.
Here, t is not defined, either, but it would usually be used to represent years in a situation like this. (In other situations, it might represent months, hours, or millenia.)
Hence, the appropriate choice is the one that describes a 4% annual increase.
Answer:
In general, an expression is in simplest form when it is easiest to use.
Step-by-step explanation:
Answer:
![\Sigma_{k=1}^{n}[3(\frac{10}{9} )^{k-1}]](https://tex.z-dn.net/?f=%5CSigma_%7Bk%3D1%7D%5E%7Bn%7D%5B3%28%5Cfrac%7B10%7D%7B9%7D%20%29%5E%7Bk-1%7D%5D)
Step-by-step explanation:
A geometric sequence is a list of numbers having a common ratio. Each term after the first is gotten by multiplying the previous one by the common ratio.
The first term is denoted by a and the common ratio is denoted by r.
A geometric sequence has the form:
a, ar, ar², ar³, . . .
The nth term of a geometric sequence is 
Therefore the sum of the first n terms is:
Given a geometric series with a first term of 3 and a common ratio of 10/9, the sum of the first n terms is:
Answer:
Step-by-step explanation:
We khow that A is the sum of all odd numbers that are less than 100
So A= 1+3+5+...+99
We can calculate this sum without adding all this numbers one by one
A = the number of terms *( first term + last one ) over 2
To get the number of terms we substract the first term from the last term then we add one
We khow that odd numbers are wiritten this way : 2*n +1 where n is an integer
So 99= 2*49+1
1= 2*0+1
So the number of terms is : 49-0+1 =50
So A= 50*(1+99)/2 = 2500
Foloowing the same method we get :
B= (49-1+1)*(2+98)/2= 2450
A>B
Answer:
x^2 - 6x + 9.
Step-by-step explanation:
f(x) = x^2 and g(x) = x - 3.
To find f(g(x)) we replace the x in f(x) by g(x).
f(g(x)) = (x - 3)^2
= x^2 - 6x + 9.
