In 1990, Nigeria had a population of about 95.3 million. E there were about 122.4 million people, an increase of about $$ 28.4 \% $$. During that decade, the population can be reasonably modeled by an exponential function. 1. Express the population of Nigeria, $$ f(x) $$ in millions of people, decades since 1990 .

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To model the population growth of Nigeria using an exponential function, let's define the variables and use the given data:

- **Initial Population ($$ f(0) $$)**: In 1990 ($$ x = 0 $$ decades since 1990), the population was **95.3 million**.
- **Population After One Decade ($$ f(1) $$)**: In 2000 ($$ x = 1 $$ decade since 1990), the population increased to **122.4 million**, which is a **28.4%** increase from 1990.

The general form of an exponential growth function is:

$$
f(x) = f(0) \times (1 + r)^x
$$

Where:
- $$ f(x) $$ is the population at $$ x $$ decades since 1990.
- $$ f(0) $$ is the initial population.
- $$ r $$ is the growth rate per decade.
- $$ x $$ is the number of decades since 1990.

Given the 28.4% increase over one decade, the growth rate $$ r $$ is 0.284. Plugging in the values:

$$
f(x) = 95.3 \times (1 + 0.284)^x
$$
$$
f(x) = 95.3 \times (1.284)^x
$$

**Final Exponential Model:**

$$
f(x) = 95.3 \times (1.284)^x
$$

Where:
- $$ f(x) $$ is the population in millions,
- $$ x $$ is the number of decades since 1990.

**Example Calculation:**
- To find the population in 2010 ($$ x = 2 $$):
$$
f(2) = 95.3 \times (1.284)^2 \approx 95.3 \times 1.648 \approx 156.9 \text{ million}
$$

This model assumes that the growth rate remains constant each decade.

**Final Answer:**

After simplifying, an exponential model is

f(x) = 95.3 × (1.284)^x,

where x is the number of decades since 1990.
The population of Nigeria can be modeled by the exponential function: $$ f(x) = 95.3 \times (1.284)^x $$ where $$ x $$ is the number of decades since 1990.

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