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 404040 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, ttt years from today.

Answer 1

The quantity after t years 40 (0.65)^{\textrm t} millions tons

Explanation:

Given as :

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 = A millions tons

Now, According to question

The quantity of carbon dioxide emitted after t year = The quantity of carbon dioxide emitted this year ×

Or, A millions tons = 40 millions tons ×

Or, A millions tons = 40 millions tons ×

Or, A millions tons = 40 millions tons ×

Answer 2

At t years, the composition of carbon dioxide is 45 * 0.35^(t - 1) million tons

Explanation:

Given

Current composition of carbon dioxide = 40million tons

Rate of reduction = 35%

Time = t years

The question is an arithmetic progression, asking is to calculate the nth term

To solve this, we make use of the geometric progression formula of nth term

Tn = a,r^(n-1)

Where a = first term

n = expected term

r = common ratio.

In this case

a = 45 million

r = 35% = 0.35

n = t

By substituton

At t years, the composition of carbon dioxide is 45 * 0.35^(t - 1) million tons