Question

In 2009, India consumed 20 exajoules of energy from all sources. (One exajoule is 1018 joules.) It is anticipated that energy requirements for India will increase by 8% per year for the foreseeable future.†

(a)
Make an exponential model for India that shows energy requirements E, in exajoules, t years after 2009.

Answer 1

The model can be written as
`E_t` = 20 *
`10^{18`
`e^{0.08t`

An exponential model is a mathematical representation of a process that exhibits exponential growth or decay.

Processes like population growth, radioactive decay, compound interest, and the spread of infectious diseases are frequently described by exponential models. They are widely used in many different fields, particularly when the rate of change is proportionate to the current value.

We know that the energy consumed in 2009 is 20 *
`10^{18`

The increase per year is 8% or 0.08

Let the Energy consumed at time t be
`E_t`

`E_t` = 20 *
`10^{18`
`e^{0.08t`