Question

Let f(x)=81+3e−0.7x .

What is the value of f(3) ?



Round the answer to the nearest hundredth.

Enter your answer in the box.

Answer 1

ANSWER


`f(3) = 87.02`

Step-by-step explanation

The given expression is


`f(x) = 81 + 3e - 0.71x`

We want to find the value of

`f(3)`

This means that, we need to substitute

`x = 3`
into the above expression and simplify.

Also, recall that,

`e \approx2.7182`

On substitution, we obtain,


`f(3) = 81 + 3(2.7182)- 0.71(3)`


`f(3) = 81 + 8.1546- 2.13`


`f(3) = 87.0248`

Rounding to the nearest hundredth gives,


`f(3) = 87.02`

Answer 2

The value of f(3) can be calculating by putting the variable x equal to 3 , x=3 which gives:
f(3)=81+3e-0.7*3=81+3e-2.1
But there is one more unknown in the equation e. e is a constant called Euler's number, after the Swiss mathematician Leonhard Euler.
e=2.7182818284590.....
Rounding to the nearest hundredth the thousandths place is used to determine whether the hundredths place rounds up or stays the same.
Rounding the Euler's constant to the nearest hundredths gives:
e=2.72
So, f(3)=81+3*2.72-2.1=81+8.16-2.1=87.06