The world population at the beginning of 1990 was 5.3 billion. assume that the population continues to grow at the rate of approximately 2%/year and find the function q(t) that expresses the world population (in billions) as a function of time t (in years), with t = 0 corresponding to the beginning of 1990.(a) if the world population continues to grow at approximately 2%/year, find the length of time t0 required for the population to triple in size.
t0 = 1 yr
(b) using the time t0 found in part (a), what would be the world population if the growth rate were reduced to 1.1%/yr?

a). 55.47 years

b). population = 9.72 billion

Step-by-step explanation:

Since population growth is an exponential phenomenon, population after t years will be represented by,

[Since rate of population growth is 2%]

Where = Population after t years

= Population at t = 0 years

A). Now we have to find the time by which the population will triple in size.

Therefore, for

By taking log on both the sides of the equation.

0.4771212 = tlog(1.02)

0.4771212 = t(0.0086)

t =

 = 55.47 years

B). If growth rate was reduced to 1.1% per year then we have to find the world population after t = 55.47 years and = 5.3 billion

              = 5.3×1.8346

              = 9.72 billion

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.