Question

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 canbe reasonably modeled by an exponential function.Express the population of Nigeria p, in millions of people,d decades since 1990.f(d) = Write an expression to represent the population of Nigeriain 1996.****Submit and Explain

Answer 1

Answer:
`\begin{gathered} An\text{ expression that represents the population of Nigeria p in d decades since 1990} \\ p\text{ = 95.3\lparen1 + 0.284\rparen}^d \end{gathered}`
`\begin{gathered} An\text{ expression to represent the population of Nigeria in 1996:} \\ p\text{ = 95.3\lparen1.284\rparen}^(0.6)\text{ } \end{gathered}`

Step-by-step explanation:

Given:

In year 1990, total population = 95.3 million

In year 2000, total population = 122.4 million

To find:

express the population p in millions of people d decades since 1990

The exponential function is given as:

`\begin{gathered} y\text{ = ab}^x \\ for\text{ rate of growth:} \\ y\text{ = a\lparen1+r\rparen}^x \\ \\ In\text{ this situation:} \\ y\text{ represesnts population} \\ y\text{ = p} \\ x\text{ represents the number of decades} \\ x\text{ = d} \\ rate\text{ of growth = r = 28.4\%} \\ r\text{ = 0.284} \end{gathered}`
`\begin{gathered} The\text{ situation in exponential function:} \\ p\text{ = a\lparen1 + r\rparen}^d \end{gathered}`
`\begin{gathered} a\text{ = inital population} \\ a\text{ = 95.3} \\ An\text{ expression that represents the population of Nigeria p in d decades since 1990} \\ p\text{ = 95.3\lparen1 + 0.284\rparen}^d \end{gathered}`
`\begin{gathered} p\text{ = 95.3\lparen1.284\rparen}^d \\ In\text{ 1996, d = 6/10 = 0.6} \\ 1996\text{ is 6 years after 1990} \\ p\text{ = 95.3\lparen1.284\rparen}^(0.6)\text{ } \\ \\ An\text{ expression to represent the population of Nigeria in 1996:} \\ p\text{ = 95.3\lparen1.284\rparen}^(0.6)\text{ } \end{gathered}`