Question

ALGEBRA 1. MEDAL!

Grisham is considering the three situations below.
I. For the first 28 days, a sunflower grows at a rate of 3.5cm per day.
II. The value of a car depreciates at a rate of 15% per year after it is purchased.
III. The amount of bacteria in a culture triples every two days during an experiment.

Which of the statements describes a situation with an equal difference over an equal interval?

Answer 1

@phi

Answer 2

They are asking which sequence of numbers is "arithmetic" as opposed to which is geometric

an arithmetic sequence changes by a fixed amount. for example
1,2,3
each term is 1 more than the previous term

geometric means the numbers are multiplied by a constant factor
for example
1,2,4,8
each is 2 times the previous.
This sequences are "exponential"

Answer 3

i don't understand

Answer 4

if it helps, you should learn that populations grow exponentially
money that earns interest grows exponentially

Answer 5

for the sunflower, assume it starts as a seed, with zero height.
can you list its height for the first few days?

Answer 6

day 1 - 0
day 2 - 3.5cm
day 3 - 7 cm
...

Answer 7

now think about
" equal difference over an equal interval?"
an "equal interval" could be "1 day"
how much does the sunflower's height change in 1 day?
3.5 cm
0, 3.5, 7, 10.5...
the difference between any pair is 3.5 cm, and the "interval" is 1 day

Answer 8

the other choices will not have an "equal difference" (because "exponential growth" which is what they have, has an "equal multiplier"... that is different)

Answer 9

i still can't understand the difference between those two.

Answer 10

The value of a car depreciates at a rate of 15% per year after it is purchased.

that is a complicated way to say that the car starts at some price, call it P (or 100 if you don't like letters)
the next year it is 15% less, P(2) = P-0.15 P or (1-0.15)P (if you know algebra)
or P(2)= 0.85* P
and the year 3, we would have P(3)= 0.85*0.85*P
we are multiplying by 0.85 to get the next year

that is different from say
P(2) = P- 10
where we subtract off 10 each time.

Answer 11

so the car depreciating is exponential decay right?

Answer 12

yes. and if its exponential (decay or growth) then it's *not* arithmetic
(and arithmetic means a "constant difference" )

Answer 13

and when it is not arithmetic then it is not going in equal intervals right?

Answer 14

yes. by "equal intervals" they mean from term 1 to term 2, term 2 to term 3, etc

Answer 15

and the fact that it's tripling every two days would not go at a constant rate right? like how it's going with the rate of 3.5cm per day.

Answer 16

yes. if it triples every 2 days, then the sequence (starting at 1) would be
1,3,9,27...
and an "equal interval" is 2 days (between numbers)
and the differences are 2,6,18
clearly not equal differences

Answer 17

okay so equal differences would be the same number of difference within the same period of time (like days, weeks, etc.)

Answer 18

yes, and if for example, you checked the sunflower case, and checked the difference between every 2 days, it would be 7 cm between any two days.

Answer 19

thanks! can u help me with a couple more of algebra 1? it's in prep for my regents.

Answer 20

if you make a new post.

Answer 21

okay