Answered

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3 point
The population of a small town over four years is recorded in the chart
below, where 2013 is represented by x= 0. The population, P(x), for these
years can be modeled by the function P(x) =aby, where bis rounded to the
nearest thousandth. Whkh statements about the function are true?

Sagot :

raphealnwobi

Answer:

1) I and III

Step-by-step explanation:

The equation of an exponential function is given by:

y = abˣ

where x is an independent variable, y is a dependent variable, a is the initial value of y (that is value of y at x = 0), b is greater than 1 for an exponential growth while b < 1 for an exponential decay.

Given that x represent years and P(x) represent population. 2013 is represented by x= 0, hence:

At the year 2013 (x = 0), the population is 3810, hence a = 3810.

The equation becomes:

P(x) = 3810(b)ˣ

At 2014 (x = 1), the population is 3943. Hence:

3943 = 3810(b)¹

3810b = 3943

b = 1.035.

Therefore a = 3810, b = 1.035. The correct option is 1) I and III

Since b > 1, this is an exponential growth.

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