Solve the Problem $\mathrm { D }$ Of a Sound Is Related to Its Intensity

Multiple Choice

Solve the problem.
-The decibel level $\mathrm { D }$ of a sound is related to its intensity $\mathrm { I }$ by $\mathrm { D } = 10 \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ . If $\mathrm { I } _ { 0 }$ is $10 ^ { - 12 }$ , then what is the intensity of a noise measured at 78 decibels? Express your answer in scientific notation, rounding to three significant digits, if necessary.

A) $7.8 \times 10 ^ { - 10 } \mathrm { Watt } / \mathrm { m } ^ { 2 }$
B) $2.44 \times 10 ^ { 15 }$ watt $/ \mathrm { m } ^ { 2 }$
C) $6.31 \times 10 ^ { - 4 }$ watt $/ \mathrm { m } ^ { 2 }$
D) $6.31 \times 10 ^ { - 5 }$ watt $/ \mathrm { m } ^ { 2 }$