The proof of this can be get with a slight modification. It can be prove that every bounded is convergent, If (an) is an increasing and bounded sequence, then limn → ∞an = sup{an:n∈N} and if (an) is a decreasing and bounded sequence, then limn→∞an = inf{an:n∈N}.
Secant
Remember it by linking the third letter:
SeCant = 1/Cos
CoSecant = 1/Sin
CoTangent = 1/Tan
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula

1) 
2) In order to find salary in 5 years we need to plug n=5, we get

= 50000(1.21550625)
<h3>=$60775.3125.</h3>
3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

Plugging n=10, a = 50000 and r= 1.05.


= 628894.62678.
<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>
The exponential equation that gives the number of bees in week 12 is of:

<h3>What is an exponential function?</h3>
It is modeled by:

In which:
In this problem, considering that the initial week is the first, and the value triples every week, the expression for the number of bees after x weeks is given by:

Hence, after 12 weeks, the expression is:

More can be learned about exponential equations at brainly.com/question/25537936
Answer:
y=8x
Step-by-step explanation:
Hope this helps you