Math / Calculus

QuestionQuestion 12
Evaluate the function. Round answers to four decimal places, if necessary. $\begin{array}{l} f(x)=e^{x}, \text { for } f(2) . \\ f(2)=\square \end{array}$ $\square$ Question Help: ${ }^{-1}$ Written Example Submit Question

Studdy Solution

STEP 1

What is this asking? We need to find the value of the function $f(x) = e^x$ when $x = 2$ . Watch out! Make sure you're using the correct value for e and round to four decimal places at the very end!

STEP 2

1. Evaluate the function

STEP 3

We're given the function $f(x) = e^x$ and we're asked to find $f(2)$ .
This means we need to substitute the value $x = 2$ into the function.
It's like plugging in a number into a formula!
Let's do it!

STEP 4

Substituting $x = 2$ into $f(x) = e^x$ , we get $f(2) = e^2$ .
Now, we know that e is approximately equal to $2.71828$ , but we'll use a calculator to get a more precise value for $e^2$ .
So, $f(2) = e^2 \approx \textbf{7.389056}$ .

STEP 5

The problem asks us to round to four decimal places.
Looking at our result $7.389056$ , the fifth decimal place is 5 or greater, so we round up the fourth decimal place.
This gives us the final answer: $f(2) \approx 7.3891$ .

STEP 6

$f(2) \approx 7.3891$

Was this helpful?

QuestionQuestion 12
Evaluate the function. Round answers to four decimal places, if necessary. $\begin{array}{l} f(x)=e^{x}, \text { for } f(2) . \\ f(2)=\square \end{array}$ $\square$ Question Help: ${ }^{-1}$ Written Example Submit Question

Studdy Solution

STEP 1

What is this asking? We need to find the value of the function $f(x) = e^x$ when $x = 2$ . Watch out! Make sure you're using the correct value for e and round to four decimal places at the very end!

STEP 2

1. Evaluate the function

STEP 3

We're given the function $f(x) = e^x$ and we're asked to find $f(2)$ .
This means we need to substitute the value $x = 2$ into the function.
It's like plugging in a number into a formula!
Let's do it!

STEP 4

Substituting $x = 2$ into $f(x) = e^x$ , we get $f(2) = e^2$ .
Now, we know that e is approximately equal to $2.71828$ , but we'll use a calculator to get a more precise value for $e^2$ .
So, $f(2) = e^2 \approx \textbf{7.389056}$ .

STEP 5

The problem asks us to round to four decimal places.
Looking at our result $7.389056$ , the fifth decimal place is 5 or greater, so we round up the fourth decimal place.
This gives us the final answer: $f(2) \approx 7.3891$ .

STEP 6

$f(2) \approx 7.3891$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? We need to find the value of the function f(x)=exf(x) = e^xf(x)=ex when x=2x = 2x=2. Watch out! Make sure you're using the correct value for *e* and round to four decimal places at the very end!

STEP 2

1. Evaluate the function

STEP 3

We're given the function f(x)=exf(x) = e^xf(x)=ex and we're asked to find f(2)f(2)f(2).This means we need to **substitute** the value x=2x = 2x=2 into the function.It's like plugging in a number into a formula!Let's do it!

STEP 4

STEP 5

The problem asks us to round to four decimal places.Looking at our result 7.3890567.3890567.389056, the fifth decimal place is 5 or greater, so we round up the fourth decimal place.This gives us the **final answer**: f(2)≈7.3891f(2) \approx 7.3891f(2)≈7.3891.

STEP 6

f(2)≈7.3891f(2) \approx 7.3891f(2)≈7.3891

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the value of the function $f(x) = e^x$ when $x = 2$ . Watch out! Make sure you're using the correct value for e and round to four decimal places at the very end!

We're given the function $f(x) = e^x$ and we're asked to find $f(2)$ .
This means we need to substitute the value $x = 2$ into the function.
It's like plugging in a number into a formula!
Let's do it!

The problem asks us to round to four decimal places.
Looking at our result $7.389056$ , the fifth decimal place is 5 or greater, so we round up the fourth decimal place.
This gives us the final answer: $f(2) \approx 7.3891$ .

$f(2) \approx 7.3891$