Questions: If f(x)=5 e^x, find f(3) rounded to the nearest tenth.

Transcript text: If $f(x)=5 e^{x}$, find $f(3)$ rounded to the nearest tenth.

Solution

Solution Steps

To find $ f(3) $ for the function $ f(x) = 5e^x $, substitute $ x = 3 $ into the function and compute the result. Then, round the result to the nearest tenth.

Step 1: Define the Function

The function is given by $ f(x) = 5e^x $.

Step 2: Substitute $ x = 3 $

To find $ f(3) $, we substitute $ x = 3 $ into the function: \[ f(3) = 5e^3 \]

Step 3: Calculate the Value

Calculating $ e^3 $ gives approximately $ 20.0855 $. Therefore: \[ f(3) \approx 5 \times 20.0855 = 100.42768461593835 \]

Step 4: Round the Result

Rounding $ 100.42768461593835 $ to the nearest tenth results in: \[ f(3) \approx 100.4 \]

Final Answer

The value of $ f(3) $ rounded to the nearest tenth is $ \boxed{100.4} $.

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