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

To represent Freedonia's carbon-dioxide emissions E(t), t years from now with a yearly reduction of 35%, use the function E(t) = 40 * (0.65)^t, where 40 million tons is the current emission and 0.65 is the remaining percentage of emissions after reduction.

Step-by-step explanation:

The student is asking to write a function that models the carbon-dioxide emissions of Freedonia in million tons, E(t), t years from today, given that the emissions are being reduced by 35% each year. The current emission level is 40 million tons of carbon-dioxide.

To create this function, we need to take into account the exponential decay of the emissions due to the percentage reduction. The general form for exponential decay is given by the equation E(t) = E_0 × (1 - r)^t, where E_0 is the initial amount, r is the rate of reduction (as a decimal), and t is the time in years. For Freedonia, E_0 is 40 million tons, and r is 0.35. Therefore, the equation becomes E(t) = 40 × (1 - 0.35)^t.

Answer 2

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

Step-by-step explanation:

Given,

Current quantity of emission, P = 40 millions,

Reduction in emission per year, r = 35% = 0.35,

Thus, the quantity of emission after t years,

`E(t)=P(1-r)^t`

`E(t) = 40(1-0.35)^t`

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

Which is the required function.