A population numbers 11000 organisms initially and grows by...

A population numbers 11,000 organisms initially and grows by 2.4% each year. Suppose P represents population, and t represents the number of years of growth. An exponential model for the population can be written in the form P = a * b^t.

Transcript

00:01 Hi there, so for this problem, we have an initial population that is given and that initial population is 11 ,000.

00:13 Now with that said, and the condition that we are given is that the population at a times t plus one, because we are told that this is each year, it decreases by 2 .4%.

00:37 So that will be, well, let me say that this is the condition when the time, so after a year, the population is then the initial amount, 11 ,000, and this minus 0 .024 times that initial value.

01:04 So from this we obtain a value of 10 ,736.

01:20 So this is the population after a year.

01:26 Okay? now, suppose that p represents the population and the times d the number of years of decline.

01:35 An exponential motor for the population can be written as, a comes on a times b and this elevated to the time.

01:45 So we need to determine the value of a and the value of b.

01:50 Now to determine the value of the value of a, we can use the condition that the population at a time equals to 0 is 11 ,000.

02:00 So if we evaluate this up 0, we will have that this is a times b, elevated up 0, so we know that something elevated up 0 is just 1.

02:10 So from this we obtain that a is immediately 11 ,000.

02:17 So now we will have that the population now becomes 11 ,000, and this times b elevated to the time.

02:27 Now to obtain the value of b, we can use the other condition that after the year, the population is 10 ,736...

Question

A population numbers 11,000 organisms initially and grows by 2.4% each year. Suppose P represents population, and t represents the number of years of growth. An exponential model for the population can be written in the form P = a * b^t.

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