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Use a calculator with a key or a A key to solve the following.
The exponential function f(x)=555(1.026) models the population of a country, f(x), in millions, x years after 1971. Complete parts (a)-(e).
a. Substitute 0 for x and, without using a calculator, find the country's population in 1971.
The country's population in 1971 was 555 million.
b. Substitute 27 for x and use your calculator to find the country's population, to the nearest million, in the year 1998 as modeled by this function.
The country's population in 1998 was 1110 million.
c. Find the country's population, to the nearest million, in the year 2025 as predicted by this function.
The country's population in 2025 will be million.



Answer :

kirigayuuki02
Given the exponential function \( f(x) = 555(1.026)^x \) models the population of a country in millions, where \( x \) is the number of years after 1971:

### Part (a)
Substitute \( x = 0 \):
\[ f(0) = 555(1.026)^0 = 555(1) = 555 \]
So, the country's population in 1971 was 555 million.

### Part (b)
Substitute \( x = 27 \) (since 1998 is 27 years after 1971):
\[ f(27) = 555(1.026)^{27} \]

Using a calculator to find \( 555 \times (1.026)^{27} \):
\[ f(27) \approx 555 \times 2 = 1110 \]

So, the country's population in 1998 was approximately 1110 million.

### Part (c)
Substitute \( x = 54 \) (since 2025 is 54 years after 1971):
\[ f(54) = 555(1.026)^{54} \]

Using a calculator to find \( 555 \times (1.026)^{54} \):
\[ f(54) \approx 555 \times 4 = 2220 \]

So, the country's population in 2025 is predicted to be approximately 2220 million.

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