Question 266547
By saying current population, we create the coordinate: (0, 15000). We put that into
(i) {{{P(t) = 1 + ke^(0.12t)}}}
to get
(ii) {{{15000 = 1 + ke^(0.12*0)}}}
which is simply
(iii) {{{1500 = 1 + k}}}
so k = 14999
Now, we rewrite the equation with our new k to get
(iv) {{{P(t) = 1 + 14999e^(0.12*t)}}}
We are given 37000 as our new population number, place that into the equation and solve for t. we get
(v) {{{37000 = 1 + 14999e^(0.12*t)}}}
subtract 1 and then divide by 14999 to get
(vi) {{{2.46676 = e^(0.12*t)}}}
take an "LN" of both sides to get
(vii) {{{.902907 = (0.12*t)}}}
divide to get
(viii) {{{t = 7.524}}} years
-----
to the nearest year, it is 8.