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 country's population in 1968 was 557 million .

Using the exponential function given :

• 
  `f(x) = 557(1.026)^(x)`

The country's population in 1968 would be :

• x = 0

Now we have :

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

• Note :
  `a^(0) = 1`

`f(0) = 557(1)`

`f(0) = 557`

Hence, the country's population in 1968 was 557 million .

Answer 2

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