Walking Speed
The avg. walking speed R of a person living in a city of population P in thousands is modeled by the function R(P)=0.37 times ln P + 0.05. where R is in feet per second. The populatin of Boston is 532,000, find the average walking speed of people living in boston.
R(P) = .37 ln P + .05
when P = 532
walking speed = .37ln 532 + .05 = 2.372 ft/s ?????
Well, looks like we need to find the average walking speed of people living in Boston. Let's plug in the population value into the function and see what we get:
R(532) = 0.37 * ln(532) + 0.05
Now, let me grab my calculator...
*typing sounds*
Alright, the answer is... approximately 0.675 feet per second. So, the average walking speed of people living in Boston is 0.675 feet per second. But be careful, Bostonians might be walking a bit faster if they're running away from scary clowns like me!
To find the average walking speed of people living in Boston, we can use the given function R(P) = 0.37 ln P + 0.05, where P represents the population in thousands.
Given that the population of Boston is 532,000, we need to convert this value to thousands by dividing it by 1,000.
532,000 ÷ 1,000 = 532
Now we can substitute the population value into the function:
R(532) = 0.37 ln 532 + 0.05
To calculate the natural logarithm of 532, we can use a calculator:
ln 532 ≈ 6.276
Substituting this value back into the equation:
R(532) = 0.37(6.276) + 0.05
Calculating the expression:
R(532) ≈ 2.318 + 0.05
R(532) ≈ 2.368
Therefore, the average walking speed of people living in Boston is approximately 2.368 feet per second.
To find the average walking speed of people living in Boston, you need to substitute the population value of Boston, P = 532,000, into the function R(P) = 0.37ln(P) + 0.05.
Step 1: Substitute the population value into the function:
R(532,000) = 0.37ln(532,000) + 0.05
Step 2: Use a calculator to find the value of ln(532,000):
ln(532,000) ≈ 13.182
Step 3: Substitute the value of ln(532,000) back into the function:
R(532,000) = 0.37(13.182) + 0.05
Step 4: Calculate the expression:
R(532,000) ≈ 4.866 + 0.05
Step 5: Simplify the expression:
R(532,000) ≈ 4.916
Therefore, the average walking speed of people living in Boston is approximately 4.916 feet per second.