Answer:
Given,
The initial population, P = 87,000,
Annual rate of increasing, r = 1.9 %,
a) Thus, the population after t years,
[tex]A=P(1+\frac{r}{100})^t[/tex]
[tex]A=87000(1+\frac{1.9}{100})^{t}[/tex]
[tex]=87000(1+0.019)^t[/tex]
[tex]=87000(1.019)^t[/tex]
[tex]87000(1.019)^t=87000e^{kt}[/tex]
Where, k is the rate constant,
By comparing,
[tex]\implies k=log(1.019)=0.00817418400643\approx 0.00817[/tex]
Hence, the approximate value of k is 0.00817.
And, the exponential growth function would be,
[tex]A=87000e^{0.00817t}[/tex]
b) If A = 145,000,
[tex]145000=87000(1.019)^t[/tex]
By using graphing calculator,
We get,
[tex]t=27.14\approx 27[/tex]
The year after 27 years from 2016 is 2043.
Hence, in 2043 the population reach 145,000.
