Question

The intensity of light emitted by a firefly can be determined by $L\left(t\right)=10+0.3t+0.4t^2-0.01t^3$, where $\left(t\right)$ is temperature in degrees Celsius and $L\left(t\right)$ is light intensity in lumens. If the temperature is $30{}^{\circ }C$, find the light intensity.

Short answer

The light intensity at temperature $30{}^{\circ }C$ is $109$ lumens.

Step-by-step solution

Step 1. Write down the given information.

The intensity of light $L\left(t\right)$ in lumens, where $\left(t\right)$ is temperature in degrees Celsius is given as:

$L\left(t\right)=10+0.3t+0.4t^2-0.01t^3....\left(1\right)$

Step 2. Calculation.

The light intensity $L\left(t\right)$ at temperature 30 degrees Celsius can be obtained by plugging $t=30{}^{\circ }C$ in (1). Therefore, from (1),

$\begin{array}{c}L\left(30\right)=10+0.3\left(30\right)+0.4{\left(30\right)}^2-0.01{\left(30\right)}^3\\ =109\text{lumens}\end{array}$

Step 3. Conclusion.

The light intensity at temperature $30{}^{\circ }C$ is $109$ lumens.