#### Question

# 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.

#### Answer

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.

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

answers

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

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