The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P0

the initial population P₀ was  5938 people

Step-by-step explanation:

since the rate of increase of the population is proportional to the population itself, then the corresponding equation for a population P and time t is

dP/dt = k*P , where k= proportionality constant

dP/P = k*dt

∫dP/P =∫ k*dt

integrating between time t=0 (with P=P₀) and time t=t (with P=P)

ln (P/P₀)=k*t

if the population doubled , so P=2*P₀ at t=5 years then

ln (2*P₀/P₀)=k*5 years

k = ln 2 / 5 years

then the population is P=9000 for t= 3 years

ln (9000/P₀)=k*3 years

ln (9000/P₀)=ln 2 / 5 years *3 years

solving for P₀

P₀ = 9000 people * e^ (- ln 2 / 5 years *3 years ) = 9000 people *2 ^(-3 years / 5 years) = 5937.78 people ≈   5938 people

therefore the initial population P₀ was  5938 people

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: