Question

The country of Freedonia has decided to reduce its carbon-dioxide emission by

35
%
35%35, percent each year. This year the country emitted
40
4040 million tons of carbon-dioxide.
Write a function that gives Freedonia's carbon-dioxide emissions in million tons,
E
(
t
)
E(t)E, left parenthesis, t, right parenthesis,
t
tt years from today.
E
(
t
)
=

Answer 1

`\\E(t) =40(0.65)^(t)`

Explanation:

Since the country wants to reduce the emission by the percentage each year, the function will be decaying function. The formula of decaying function will look like this

`E(t) =E_(0) (1-r)^(t)\\`

Where

E(t) = the number of emission after t years

E0= the number of initial emission= 40 million tons

r=rate of growth/decay = 35%= 0.35

t= time in years

If we put the number, the equation will be:

`E(t) =E_(0) (1-r)^(t)\\E(t) =40(1-0.35)^(t)\\E(t) =40(0.65)^(t)`