Question

In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.
(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.

Answer 1

your ordered pair will be (time, temperature) where t=0 corresponds to 1870.... so t=99 corresponds to 1969:

(0, 11.8)
(99, 13.5)

you need to come up with an equation of a line that passes through both these points...
ok so far?

Answer 2

yea

Answer 3

are you familiar with point-slope form: \(\large y-y_1=m(x-x_1) \) ???
we can use this for the equation of the line you need...

Answer 4

so first, let's calculate slope, \(\large m=\frac{y_2-y_1}{x_2-x_1}=\frac{13.5-11.8}{99-0}= \) ???

Answer 5

my book used (1870,11.8) and (1969, 13.5) as points in the demo of this problem
T should equal T-13.5=(13.5-11.8)/(1969-1870) (t-1969)
the books answer was T=0.01717t^2-20.31

Answer 6

the answer didnt work when i used it to answer this problem in my hw

Answer 7

"T=0.01717t^2-20.31"
why is the t^2 ??

it should be T=0.01717t-20.31

Answer 8

i think it might be a typo in the book. the t^2 confused me

Answer 9

it is a typo.... this cannot be a quadratic function....

Answer 10

the answer still does not work :(

Answer 11

that's because they want t=0 to correspond with 1870, and t=99 with 1969...

Answer 12

the screenshot if what the book worked out

Answer 13

*is

Answer 14

they basically used point-slope form for the equation of the line....

Answer 15

"the answer didnt work when i used it to answer this problem in my hw"
what is the problem you're trying to answer?

Answer 16

the one i posted

Answer 17

ok... so instead of using
(0, 11.8)
(99, 13.5)

the book used
(1870, 11.8)
(1969, 13.5)

these two points will yield the same slope but in terms of the variable time t, mines starts at the origin (time = 0) while theirs start at t=1870

Answer 18

ok

Answer 19

their answer (the one your book posted): T=0.01717t-20.31 is the equation of the line with t being the year NOT the amount of years after 1870...

Answer 20

so i have to find the other equation

Answer 21

not that hard really... slope is the same, m=0.01717.
and we can use the first point , (0, 11.8) as the point we'll put into point-slope form

Answer 22

\(\large y-y_1=m(x-x_1) \)
\(\large y-11.8=(0.0717)(x-0) \)
\(\large y=(0.0717)(x-0)+11.8 \)
\(\large y=0.0717x+11.8 \)

that x should be the t and the y should be T

Answer 23

*slope = 0.01717

Answer 24

thanks you are very helpful :)

Answer 25

yw... :)

Answer 26

i had to make the slope a fraction for it to work :)