Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?
Choose 1
Choose 1

(Choice A)
A
42{,}000\left(\dfrac{1-0.04^n}{0.96 }\right)42,000(
0.96
1−0.04
n


)42, comma, 000, left parenthesis, start fraction, 1, minus, 0, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice B)
B
42{,}000\left(\dfrac{1-1.04^n}{-0.0 4}\right)42,000(
−0.04
1−1.04
n


)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, minus, 0, point, 04, end fraction, right parenthesis

(Choice C)
C
42{,}000\left(\dfrac{1-1.04^n}{0.96 }\right)42,000(
0.96
1−1.04
n


)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice D)
D
42{,}000\left(\dfrac{1-0.96^n}{-0.0 4}\right)42,000(
−0.04
1−0.96
n


)

Step-by-step explanation:

This is a compound interest formula expressed as:

Where:

#We substitute the given values to determine amount after n years as follows:

Hence, the amount earned after n years is given by the expression

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

do have an equation or graph or

step-by-step explanation: