Question

Please help, unsure of how to set up. Will give medal & fan!
Thomas is earning $50,000 a year as an accountant. He automatically receives a 2 & 1/2 % raise every year. How much is his salary in one year? five years? twenty years? fifty years?

Answer 1

50,000*.025 = 1250.
First year would be 50,000+1,250 = 51,250.

Answer 2

So I just keep multiplying by 0.25? for the second one would i just do 50,000*0.025(5)

Answer 3

I forgot the formulas for this, but you can consistently do this. :o

Answer 4

No, it does not work like how you said.

Answer 5

well shoot :(

Answer 6

The overall number changes every time.

Answer 7

51250 * .025 for second year.

Answer 8

so i just keep doing that until i reach 5?

Answer 9

y = a(1 + r)x

Answer 10

where:
y = value of the variable after x periods (future compounded value)
a = initial value of the variable
r = compound growth rate
x = number of periods

Answer 11

y = 50000(1 + 0.025)^5

Answer 12

y = 56750.41064 for 5 years. The exponent is the number of periods.

Answer 13

Now, just do y = 50000(1 + 0.025)^20 and y = 50000(1 + 0.025)^50

Answer 14

put it in my calculator and got the same thing (: okay!

Answer 15

Try ^20 and ^50. This accounts for the year periods.

Answer 16

for 20 i got 81,930.82201

Answer 17

81930.8220145, so yes correct.

Answer 18

when i tried to do 50 it did something weird

Answer 19

Scientific notation?

Answer 20

x10?

Answer 21

it says 7.88860905E-81

Answer 22

y = 50000(1 + 0.025)^50
Try again. That was not correct.

Answer 23

okay lol not sure what i did wrong. now i got 171,855.436

Answer 24

That is correct, good job.

Answer 25

thank you so much!!

Answer 26

do you happen to know what to do for the same situation, except a percentage decrease? would i just make the ^# negative?

Answer 27

Hmm.

Answer 28

One second.

Answer 29

like the question is
lorenzo and ashton both earn $46,000 a year. lorenzo must have done something to make his boss angry bc he will now get a decrease of 1.75% every year from now on. however, ashton must be a perfect employee bc she will get a 1.75% increase every year from now on.
and i'm just supposed to write equations to determine each of their salaries after n years.

Answer 30

Well, for Ashton, it would be y = 46000(1+.0175)^n

Answer 31

okay! i figured lorenzo's equation would be y=46000(1-.0175)^n but I'm not really sure

Answer 32

There's a different equation for decaying exponential.

Answer 33

P(t) = P0e-rt

Answer 34

where:
P(t) = the amount of some quantity at time t
P0 = initial amount at time t = 0
r = the decay rate
t = time (number of periods)

Answer 35

P(n) = 46000e^-0.0175(n)

Answer 36

so -0.0175(n) would all be an exponent?

Answer 37

No, sorry, it shouldn't be negative.

Answer 38

P(n) = 46000*0.0175(n)

Answer 39

Example: P(2) = 46000*0.0175(2) = 1600. 46000-1600 = 44400.

Answer 40

You're awesome! Thank you so much.

Answer 41

Of course, anytime.