# Math help is really aprciated ? THanks !?

im quiet stuck on this problem its exponetial growth and decay thanks so much ill make sure i choose best awnser so u get points thanks!

3.) Suppose the population of a town is 3,400 in 2000. The population decreases at a rate of 2% every 20 years. What will be the projected population in 2040? Round your answer to the nearest whole number.

4.)

The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number.

5.)You invest an initial \$2,000 in an account that has an annual interest rate of 6%, compounded daily. How much money will you have in the account after 15 years? Round your answer to the nearest whole number.

Hey Jazzy,

Most would solve the firt problem by hand

2000 3400

2020 3400-.02*3400=3360

2040 3360-.02*3360=3292.8

Round to 3293

We could do the same for the next problem, but we'd have to calculate 10 years. So we find a formula instead.

Let time t=0 be the intial year (2000)

The population p is a function of the year t

p(t)=430*(1.009)^t

When t=0, 1.009^0 equals 1, so we have our initial population of 430

The next year, we have .9% more. or 430*1.009.

When t=2, we have (430*1.009)*1.009. that's .9% growth from p(t=1)

when t=3, we have (430*1.009)*1.009*1.009. that's .9% growth from p(t=2)

We don't have to do the calculations now that we have a formula.

In 2010, t=10, so p(10)=430*1.009^10.

Plugging than into my calculator, I get 430*1.093734. About 470.30.

Round to 470.

#1

3.) P = 3400 (0.98)^(t/20)

P = 3400 (0.98)^2 = 3265.36 ≈ 3265

4.) P = 430 (1.009)^t

P = 430 (1.009)^10 = 4770.3055653... ≈ 4770

5.) A = 2000 (1 + 0.06/365)^(365 ? 15) = 4918.842388... ≈ \$4919

#2

1).from 2000-2020

decrease= 2%of 3400=78

net population=3400-78=3322

from 2020-2040

decrease=2%3322=66.4(or 66)

net=3322-66

#3

use the formula of compound interest

C.I=P(1-R/100)^n

as the population decreases

=3,400(1-2/100)^20

3,400(98/100)^20

using calculator or log tables simplify the above and subtract with 3,400

4)

same formula since here poulation increses use P(1+R/100)^n

430(1+.9/100)^10

using calculator or log table find the value and add with 430

5) use the above method and add

#4