Originally Posted by

**Unt0t** ...

(B) In 1990, the number of families living below the poverty line was 33,585,000 families. By 1991, the number had increased 6%.

(i) Write a function of the form P(t) = P__0__a^t to model this growth, where P(t) is the population *t* years after 1990.

(ii) How many families will be living below the poverty line now (2007) according to this model?

(iii) When will the number of families living below the poverty line reach 1 billion if the growth continues at 6%?

...

Hello, UntOt,

(i)

if the relative increase is 6% then the factor (1 + 0.06) is the base of the function. Thus:

P(t) = 33,585,000 * (1.06)^t

(ii) from 1990 to 2007 you have t = 17. Calculate

P(17) = 33,585,000 * (1.06)^17 ≈ 90,436,774 . Because the initial value is exact to the thousands I would use 90,437,000.

(iii)

You know P(t) = 10^9 . Plug in this value into the equation and solve for t:

1,000,000,000 = 33,585,000 * (1.06)^t . Divide by 33,585,000

29.7752 = (1,06)^t . Use logarithm

log(29.7752) = log(1.06) * t Code:

log(29.7752)
t = ------------ ≈ 58.24 years
log(1.06)