A population grow according to an exponential growth model, with P0=40 and P1=44 Complete the recursive formula Pn=40•Pn-1 Write the explicit formula for Pn
To find the explicit formula for Pn, we can use the formula:
Pn = P0 * (1 + r)^n
where r is the growth rate.
We can find the growth rate by using the information given:
P1 = P0 * (1 + r)
44 = 40 * (1 + r)
1 + r = 44/40 = 1.1
r = 0.1
Now we can substitute P0 = 40 and r = 0.1 into the formula to get:
Pn = 40 * (1 + 0.1)^n
Simplifying:
Pn = 40 * 1.1^n
Therefore, the explicit formula for Pn is Pn = 40 * 1.1^n.
To find the explicit formula for Pn in an exponential growth model, we need to determine the common ratio (r).
From the given information, we know that P0 = 40 and P1 = 44.
We can use the formula Pn = P0 * r^n to find the common ratio (r).
Let's substitute n = 1 and solve for r:
P1 = P0 * r^1
44 = 40 * r
r = 44/40
r = 1.1
Now that we have the common ratio, we can write the explicit formula for Pn:
Pn = P0 * r^n
Pn = 40 * (1.1)^n
So, the explicit formula for Pn in this exponential growth model is Pn = 40 * (1.1)^n.