Question

Find a function that models the population after t years

Answer 1

A) You have:

$f(0) = 270000\\ f(1) = 1.04f(0), \\ f(2) = 1.04f(1) = 1.04(1.04f(0)), \\ f(t) = 1.04f(t-1) = 1.04(1.04f(t-2)) ... = 1.04^{t}f(0) = 1.04^{t}*270000$

b) $f(2004-1998) = 1.04^{2004-1998} * 270000 = 341636$

c)
$1.04^{x-1998} * 270000 \geq 534094 \\ x - 1998 \geq {ln( \frac{534094}{270000} )}/{ln(1.04)} x \geq 2015.4 x = 2016$