SOLUTION: A population grows according to an exponential growth model. The initial population is Po = 14, and the growth rate is r = 0.4. Then: P1= P2= Find an explicit formula for Pn.

Question 1175035: A population grows according to an exponential growth model. The initial population is Po = 14, and the growth rate is r = 0.4.
Then:
P1=
P2=
Find an explicit formula for Pn. The formula should involve n.
Pn=2
Use the formula to find P11
P11=
Accurate to at least 1 decimal point

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the growth rate is .4 per time period.
the expnential growth model is f = p * (1 + .4) ^ n
f is the future value.
p is the present value.
r is the growth rate per time period.
n is the number of time periods.

in p0, n = 0
in p1, n = 1
in p2, n = 2
in p11, n = 11

you are given that p0 = 14.

in the formula, that becomes f = 14 * (1 + .4) ^ 0 = 14 * 1.4 ^ 0 = 14.

the formula for p1 becomes f = 14 * (1 + .4) ^ 1 = 14 * 1.4 ^ 1 = 19.6.

the formula for p2 becomes f = 14 * (1 + .4) ^ 2 = 14 * 1.4 ^ 2 = 27.44.

the formula for p11 becomes f = 14 * (1 + .4) ^ 11 = 14 * 1.4 ^ 11 = 566.9391238.

the equation can be graphed as shown below.
first graph is for n = 0, 2, 2 which covers p0, p1, p2.
second graph is for n = 11 which covers p11.

RELATED QUESTIONS
A population grows according to an exponential growth model. The initial population is... (answered by ikleyn)

A population grows according to an {{{highlight(exponential)}}} growth model, with Po =60 (answered by ikleyn)

A population grows according to an exponential growth model. The initial population is... (answered by josgarithmetic)

A population growing according to an exponential growth model. The initial population is... (answered by ikleyn)

Here I need help on part A and B its confusing. Exponential Growth 2. A population... (answered by ikleyn)

A population grows according to an exponential growth model, with Po =20 and P1 = 24... (answered by ikleyn)

a population grows according to an exponential growth model, with P0 = 8 and P1 =... (answered by josgarithmetic)

A population grows according to an exponential growth model, with P0= 43 and P3=57.233 (answered by josgarithmetic)

The number of bacteria in a certain population increases according to a continuous... (answered by josgarithmetic)