Question

Write an exponential function showing the relationship between y and t

Answer 1

`y=500e^(0.02t)`

Explanation:

An exponential function refers to those function where its independent variable is presentes as exponent.

These functions are also known as trascendental functions, because they can be applied in many problems. One of the best known problems solved by these functions is population growth, which can be described as

`P=P_(0)e^(rt)`

Where
`P_(0)` is the initial population,
`r` is the rate of growth and
`t` is time.

Let's give it some values as an example.

`y=500e^(0.02t)`

That is, this is a function which represents and starting population of 500 with a rate of growth of 2%.

Also, this is an example of an exponential function where it's shown the relationship between
`y` and
`t`.

Therefore, the answer is
`y=500e^(0.02t)`

Answer 2

We can write an exponential function showing the relationship between y and t same as y = Aie-kt.
The Y represents the remaining value at time t.
The Ai is the initial value at time ti.
The k is the decay rate commonly expressed in the decimal value.