a recent earthquake had a magnitude (r) of 3. what would the energy (e) of the earthquake be according to…

a recent earthquake had a magnitude (r) of 3. what would the energy (e) of the earthquake be according to the given model?\n$r = 0.67\\log(0.37e) + 1.46$\n$e = ?$ kwh\nround to the nearest hundredth.

a recent earthquake had a magnitude (r) of 3. what would the energy (e) of the earthquake be according to the given model?\n$r = 0.67\\log(0.37e) + 1.46$\n$e = ?$ kwh\nround to the nearest hundredth.

Answer

Explanation:

Step1: Substitute R=3 into the model

$3 = 0.67\log(0.37E) + 1.46$

Step2: Isolate the logarithmic term

$0.67\log(0.37E) = 3 - 1.46$ $0.67\log(0.37E) = 1.54$ $\log(0.37E) = \frac{1.54}{0.67} \approx 2.2985$

Step3: Convert log to exponential form

$0.37E = 10^{2.2985} \approx 198.92$

Step4: Solve for E

$E = \frac{198.92}{0.37} \approx 537.62$

Answer:

$537.62$ kwh