the town of gilbertville increased from a population of 3562 people in 1970 to a population of 9765 in 2000. define an exponential function that models the towns population as a function of the number of years since 1970

P(t) = 3562•( 1.034)^t

Step-by-step explanation:

Here, we want to define an exponential equation.

To define the exponential equation, some key concepts are needed.

We need the initial population value which is given as; 3562

We need the growth rate per year , let’s call this r

The population at a particular year can thus be modeled as;

P(t) = I•(1 + r)^t

where t is the number of years after 1970( difference between the particular year and 1970)

Thus, to completely write the exponential equation, we need to get the value of r ( which is the growth percentage per year assuming we have a parallel growth rate of the population).

Hence;

9765 = 3562( 1 + r)^30

divide both sides by 3562

2.7414 = (1 + r)^30

Take the log to base e of both sides

ln 2.7414 = ln (1 + r)^30

ln 2.7414 = 30ln (1 + r)

1.0085 = 30 ln (1 + r)

divide both sides by 30

0.034 = ln ( 1 + r)

1 + r = e^(0.034)

1 + r = 1.034

r = 1.034 - 1

r = 0.034

So the growth percentage is about 3.4% yearly

So the exponential equation would be;

P(t) = 3562•( 1.034)^t

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation: