The average walking speed R of people living in a city of population P,in thousands, is given by R=0.37InP+0.05, where R is in feet per second.

a.) The population of Honolulu, Hawaii is 395,790. Find the average walking speed.
b.) A city's average walking speed is 2.70 ft/sec. Find the population.

Thank you. I was able to get the same answers.

a.) To find the average walking speed in Honolulu, Hawaii, we need to substitute P = 395,790 into the equation R = 0.37ln(P) + 0.05.

R = 0.37ln(395,790) + 0.05

Now, let me just do some quick calculations...

*Calculating, calculating, calculating...*

Ah, the answer is... *drumroll please*... approximately 1.88 ft/sec! So, the average walking speed in Honolulu is 1.88 feet per second. Careful not to walk too fast, you might leave the beautiful scenery behind!

b.) Now, let's play around with the equation a bit to solve for P. We have R = 2.70 ft/sec, so we set up the equation as follows:

2.70 = 0.37ln(P) + 0.05

Now, let's do a quick math magic trick...

*Waving my wand, abracadabra!*

After crunching the numbers, I can reveal that the population of the city corresponding to an average walking speed of 2.70 ft/sec is approximately 1,595,751. So lace up your walking shoes and join the lively population of this mysterious city!

a) To find the average walking speed for a population of Honolulu, Hawaii, we will substitute the given population value into the formula R = 0.37ln(P)+0.05.

Let P = 395,790 (the population of Honolulu, Hawaii)

R = 0.37ln(395.79)+0.05
= 0.37(12.88) + 0.05
= 4.7736 + 0.05
≈ 4.82 ft/sec

Therefore, the average walking speed for the population of Honolulu, Hawaii is approximately 4.82 ft/sec.

b) To find the population for a city with an average walking speed of 2.70 ft/sec, we will rearrange the formula and solve for P:

R = 0.37ln(P)+0.05

2.70 = 0.37ln(P)+0.05

Now we'll isolate the term ln(P) on one side:

0.37ln(P) = 2.70 - 0.05
= 2.65

Divide both sides by 0.37:

ln(P) = 2.65 ÷ 0.37
≈ 7.16

To eliminate the natural logarithm on the left side, we will exponentiate both sides using base e (Euler's number):

P = e^7.16
≈ 1300.234

Therefore, the population of the city with an average walking speed of 2.70 ft/sec is approximately 1,300,234.

a) To find the average walking speed for a population of 395,790 in Honolulu, Hawaii, we will substitute the given population value into the equation R = 0.37InP + 0.05.

Given: P = 395,790
R = 0.37InP + 0.05

Substituting P = 395,790 into the equation,
R = 0.37 * In(395,790) + 0.05

To solve this problem, you need to calculate the natural logarithm (In) of the population, 395,790, and then plug the result into the equation.

Using a scientific calculator or software, the natural logarithm (In) of 395,790 is approximately 12.8907.

Substituting the value of InP into the equation,
R = 0.37 * 12.8907 + 0.05

Simplifying the equation further,
R ≈ 4.7641 + 0.05
Therefore, R ≈ 4.8141 ft/sec.

So, the average walking speed for a population of 395,790 in Honolulu, Hawaii, is approximately 4.8141 ft/sec.

b) To find the population for a city with an average walking speed of 2.70 ft/sec, we will rearrange the equation R = 0.37InP + 0.05.

Given: R = 2.70 ft/sec
R = 0.37InP + 0.05

Substituting R = 2.70 into the equation,
2.70 = 0.37 * InP + 0.05

Next, we will isolate the term InP by subtracting 0.05 from both sides of the equation,
2.70 - 0.05 = 0.37 * InP

Simplifying further,
2.65 = 0.37 * InP

Now, divide both sides of the equation by 0.37 to isolate the InP term,
InP ≈ 2.65 / 0.37

Using a calculator, InP ≈ 7.1622.

To find the population P, we take the inverse of the natural logarithm of 7.1622,
P ≈ e^(7.1622), where e is the base of natural logarithm.

Using a calculator or software, the value of e^(7.1622) is approximately 1311.22.

Therefore, the population for a city with an average walking speed of 2.70 ft/sec is approximately 1311,220.

a) is just button-pushing on a calculator

I got a rate of 4.82 ft/s

b)
2.7 = .37(lnP) + .05
2.65 = .37lnP
lnP = 2.65/.37 = 7.162162
P = 1289.6

P = 1290