In 1990, Nigeria had a population of about 95.3 million. By 2000 , 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 .

To model the population of Nigeria using an exponential function, we can start by identifying the values we have. Let \( P_0 \) be the initial population in 1990, which is 95.3 million, and we know that by 2000 (a decade later), the population increased to approximately 122.4 million. Using the formula for exponential growth \( P(t) = P_0 e^{rt} \), we need to determine the growth rate \( r \). The change from 95.3 million to 122.4 million over 1 decade can be expressed as: \[ 122.4 = 95.3 e^{r} \] From this equation, you can solve for \( r \). After finding \( r \), you can express the population function as: \[ f(x) = 95.3 e^{rx} \] where \( x \) is the number of decades since 1990. Now, let's get a little more into the juicy details: If you crunch the numbers, you’d find \( r \approx 0.255 \) or about 25.5% per decade. Thus, the model becomes: \[ f(x) ≈ 95.3 e^{0.255x} \] And voilà! You've got a robust model to interpret Nigeria's population growth through the 1990s and beyond! 🏙️📈 Dive into the data, and you'll witness how exponential functions can vividly capture real-life growth, much like how a plant feeds on sunshine, expanding its leaves year by year! 🌱☀️