Question

The exponential function f(x) models the population of a country, f(x), in millions, x years after . Complete parts (a)(e).a. Substitute 0 for x and, find the country's population in The country's population in was nothing million.

Answer 1

The given exponential function is

$f(x)=557(1.026)^x$

Where x is the number of years after 1968

f(x) is the population in millions

a) Substitute x by 0

$f(0)=557(1.026)^0$

Since any number to the power of zero = 1, then

$\begin{gathered} (1.026)^0=1 \\ f(0)=557(1) \\ f(0)=557 \end{gathered}$

The population in 1968 is 557 million

b) At year, 2000 we need to find the value of x

$\begin{gathered} x=2000-1968 \\ x=32 \end{gathered}$

Now let us find f(32)

$\begin{gathered} f(32)=557(1.026)^{32} \\ f(32)=1266.399528 \end{gathered}$

Round it to the nearest whole number

Then the population in 2000 is 1266 million