Question

The country of Freedonia has decided to reduce its carbon-dioxide emission by 35% each year. This year the country emitted 40 million tons of carbon-dioxide.
Write a function that gives Freedonia's carbon-dioxide emissions in million tons, E(t), t years from today.

Answer 1

The function that gives Freedonia's carbon-dioxide emissions in million tons, E(t), t years from today:

$E(t) = 40(0.65)^t$

Solution:

The rate of decrease of carbon dioxide each other = 35%

The quantity of carbon dioxide emitted this year = 40 million tons

Let the quantity of carbon dioxide emitted after t year = E(t) millions tons

Then, the function that gives Freedonia's carbon-dioxide emissions in million tons, E(t), t years from today is given by:

$E(t) = p(1-\frac{r}{100})^t$

Where,

p is the quantity of carbon dioxide emitted this year

r is the rate of interest

t = number of years

Here,

p = 40 million tons

r = 35 %

Substituting the values we get,

$E(t) = 40(1-\frac{35}{100})^t\\\\E(t) = 40(1-0.35)^t\\\\E(t) = 40 \times 0.65^t\\\\E(t) = 40(0.65)^t$

Thus, quantity of carbon-dioxide emissions in million tons after t yaers is given by function $E(t) = 40(0.65)^t$