A population of a certain city increases exponentially at a rate of 5.7%. Initially, it is 1.84 million. After how many years will the population reach 3.21 million?

t = 10.0 years

It will take 10 years for the population to reach 3.21 million

Step-by-step explanation:

Given;

Initial population P = 1.84 million

Final population F = 3.21 million

Rate r = 5.7% = 0.057

time t = ?

The exponential growth can be expressed as;

F = P(1+r)^t

We need to make t the subject of formula;

F/P = (1+r)^t

Taking natural logarithm of both sides;

ln(F/P) = tln(1+r)

t = ln(F/P) ÷ ln(1+r)

Substituting the given values;

t = ln(3.21/1.84) ÷ ln(1+0.057)

t = 10.0 years

It will take 10 years for the population to reach 3.21 million

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c