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6) Write the equation of the exponential function after t number of years for a population that has an initial value of 245 and it doubles every 5 vears:...

Question

6) Write the equation of the exponential function after t number of years for a population that has an initial value of 245 and it doubles every 5 vears:

6) Write the equation of the exponential function after t number of years for a population that has an initial value of 245 and it doubles every 5 vears:



Answers

In Problems $5-8,$ write an exponential equation describing the given population at any time $t .$
Initial population 200 ; doubling time 5 months

So if we recall that the doubling population growth model for a population A at Time T is the equation A equals a sub zero times two to the power of T divided by D and remember that a sub zero is the initial population, and D is the doubling time. And so we are given that a sub zero is equal to 200 or the initial population is 200 the doubling time is five. And so let's start to end these values into our equation. So we get a equals 200 times, two to the power of T over five. And so the exponential equation for a population A at time T is a equals 200 times two to the power of cheat about it by five.

So an exponential model. It is defined by the equation. A equals a sub zero times two to the power of cheese about of I D and a sub zero is the initial population and deice the doubling time. And so because we're given that a subzero is 5000 and the doubling time is three, we can go ahead and plug in these values and to our known equation. So a is equal to 5000 times two to the power of T divided by three.

So the exponential growth model for a population A at time T is the equation. Egg was a sub zero times e to the Katie and a subzero. A sub zero is the initial population, and K is the growth rate. And so we are given that a sub zero is equal to 2000 or the initial population is 2000 and K is equal to 2% in decimal form, that would be 0.2 And so let's substitute in these values into our little equation and we get A is equal to 2000 times E to the 0.0 to t. And so the exponential equation for the population A at Time T is just a gal's 2000 times he to the 0.2 t.

So this question suppose you that there was 260,500 people in the in 2000 in the year 2000. And then there's now 268 1000 Etienne 2005. The next session. I want you to write an equation that in this form, So basically what we're gonna end up with is this is what we end up with. When we started with this, we started with 260,512 and then that took five years. So five k, it's very. And then if we divide, we get 1.29 is equal to each of the five K, and that's our exponential function.


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