hard word problem

Question

4. The equation S = 93log(d) + 65 relates the speed of the wind, S, in miles per hour near the center of a tornado to the distance that the tornado travels, d, in miles.

A) If a tornado travels a distance of 130 miles, find the wind speed near its center. (Round your answer to the nearest whole number.)

Answer = approximately
miles per hour


B) If a tornado has sustained wind speeds near its center of 275 mph, find the distance it can travel. (Round your answer to the nearest whole number.)

Answer = approximately
miles

Answer 1

S = 93 log (d) + 65 ;  S = wind speed;  d = distance traveled by tornado

 

A) tornado travels 130 miles = d ; find S

 

       S = 93 log₁₀(130) + 65

 

      S = 261.6 mph rounds up to 262 mph

 

 

B)  S = 275 mph ;  find d

 

                275 = 93 log₁₀ (d) + 65

 

                210 = 93 log₁₀ (d)

 

           210/93 = log₁₀ (d)

 

             2.258 = log₁₀ (d)

 

Change from Log Form to Exponential Form

 

           10^2.258 = d

 

 181.134 miles = d   Rounded is 181 miles

 

 

Answer 2

S = 93 log(d) + 65

 

A)

 

Based on the given equation, where I assume log = log₁₀, 

 

S = 93 log₁₀(130) + 65 ≅ 262 mph

 

B)

 

275 = 93 log₁₀(d) + 65

 

log₁₀(d) = (275 - 65) / 93 ≅ 2.25806

 

d = 10^2.25806 ≅ 181 mi