Acity's  population is represented by the function p=25,000 (1.0095) t , where t is time in years. how could the function be rewritten to identify the daily growth rate of the population? what is the approximate daily growth rate?

We are given the following function:

P = 25,000 (1.0095)^t

However the given function is in the basis of 1 year. We know that in 1 year there are 365 days, therefore we must place a (1/365) exponent to the overall rate (1.0095) and divide the time (t) by 365 to get a function on the basis of per day. Hence:

P = 25,000 [1.0095^(1/365)]^(t / 365)

The rate is equal to the term:

 rate = 1.0095^(1/365) – 1

Calculating for the rate:

rate = 1.000025905 – 1

rate = 0.000025905 or 0.003%

Summary of answers:

>P = 25,000 [1.0095^(1/365)]^(t / 365)

>0.003%

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions