The population of a certain city was 112,000 in 1998, and the observed relative growth rate is 4% per year. (a) Find a function that models the population after t years. (b) Find the projected population in the year 2004. (c) In what year will the population reach 200,000

See Explanation

Step-by-step explanation:

Now;

From;

P=Poe^kt

Where;

P = population at time=t

Po = population initially present

k = growth rate

t = time taken

a) The function is;

P= 112,000e^0.04t

b) In the year 2004, the population will be

P= 112,000e^0.04(6)

P= 142380

c) 200,000 =112,000 e^0.04t

200,000/112,000 =  e^0.04t

1.786 = e^0.04t

ln 1.786 = ln e^0.04t

ln 1.786= 0.04t

t = ln 1.786/0.04

t = 14.5 years

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).