Question

Jim's family recently moved to a new

city. The city's population has been
growing, and based on recent trends,
Jim expects it to continue growing
exponentially. This table shows the
expected population in the next two
years.
Time (years)

Population

840,000
882,000

Time (years)

1
2
Find an expression for P(t), the city's
population t years from now. Write your
answer in the form P(t) = a(b)t, where a
and b are integers or decimals. Do not
round.
P(t) =

Answer 1

Explanation:

city. The city's population has beengrowing, and based on recent trends,Jim expects it to continue growingexponentially. This table shows theexpected population in the next twoyears.Time (years)Population840,000882,000Time (years)12Find an expression for P(t), the city'spopulation t years from now. Write youranswer in the form P(t) = a(b)t, where aand b are integers or decimals. Do notround.P(t) =

Answer 2

To find an expression for P(t), we can use the two given data points to create a system of equations. We can assume that the population is growing exponentially, which means that the population at time t is given by:

P(t) = a(b)^t

where a and b are constants that we need to determine.

Using the first data point, we have:

840,000 = a(b)^1

which simplifies to:

840,000 = ab

Using the second data point, we have:

882,000 = a(b)^2

We can solve for a in terms of b by dividing the second equation by the first equation:

882,000/840,000 = (a(b)^2)/(ab)

Simplifying, we get:

1.05 = b

Substituting this value of b into the first equation, we get:

840,000 = a(1.05)

Solving for a, we get:

a = 800,000

Therefore, the expression for P(t) is:

P(t) = 800,000(1.05)^t

This means that the city's population t years from now can be calculated by multiplying the initial population of 800,000 by 1.05 raised to the power of t.