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Posted on Jan 02, 2017

The formula for exponential growth and exponential decay is

A =I (1 + r)^n, where A is the amount, I is the initial amount, r is the rate of exponential growth or decay and n is the number of periods.

For example, if we start with 100 units and the growth is 5% per period, we get the equation A = 100 (1+0.5) ^n. When n is 0, anything to the exponent 0 is 1, so we start with 100 units. When n is 1, we get 105 units.

Similarly, if a car costing $50,000 depreciates in value 30% per year, we have A= 50000 (1-0.3)^n, Again, when n = 0, anything to the power of 0 is 1, so we start at $50,000. When n=1, A = 35,000. When n = 2, A = $24,500.

Good luck,

Paul

A =I (1 + r)^n, where A is the amount, I is the initial amount, r is the rate of exponential growth or decay and n is the number of periods.

For example, if we start with 100 units and the growth is 5% per period, we get the equation A = 100 (1+0.5) ^n. When n is 0, anything to the exponent 0 is 1, so we start with 100 units. When n is 1, we get 105 units.

Similarly, if a car costing $50,000 depreciates in value 30% per year, we have A= 50000 (1-0.3)^n, Again, when n = 0, anything to the power of 0 is 1, so we start at $50,000. When n=1, A = 35,000. When n = 2, A = $24,500.

Good luck,

Paul

Nov 05, 2015 | Texas Instruments Ti-30Xs Multiview...

The population doubles in ten years so the annual growth is the tenth root of two. The growth in twelve years is the annual growth rate raised to the twelfth power.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

What this problem has to do with a printer, I have no idea.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

What this problem has to do with a printer, I have no idea.

Nov 05, 2012 | Office Equipment & Supplies

The population doubles in ten years so the annual growth is the tenth root of two. The growth in twelve years is the annual growth rate raised to the twelfth power.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

Nov 05, 2012 | Computers & Internet

When you buy it is worth $60, 000

I will assume that at the end of a year it is the whole new value of the house that is increased by 5%.

After**1 year** value=60,000*(1+0.05)**^1**

After**2 years** value=$60,000(1+0.05)*(1+0.05)=60,000*(1.05**)^2**

Do you see the pattern?

After**7 years,** the value of the house will be 60,000*(1.05)**^7**

However if the increase is not compounded

Then after 1 year value=60,000*(1+0.05)

After** 2** years, value=60,000*(1+0.05+0.05)=60,000*(1+**2***0.05)

After** 7 **years, value=60,000*(1+**7***0.05)

Depending on the coumpounding or not the two values will be different

With compounding: final value=$84,426.02

Without compunding: final value is $81, 000.

I showed you the possible mathematical solutions. It is now up to you to decide which is the one that applies to your case.

I will assume that at the end of a year it is the whole new value of the house that is increased by 5%.

After

After

Do you see the pattern?

After

However if the increase is not compounded

Then after 1 year value=60,000*(1+0.05)

After

After

Depending on the coumpounding or not the two values will be different

With compounding: final value=$84,426.02

Without compunding: final value is $81, 000.

I showed you the possible mathematical solutions. It is now up to you to decide which is the one that applies to your case.

Jan 28, 2012 | HP 10bII Calculator

If the interest is compounded monthly:

2nd [CLR TVM] (clear any existing results)

1 5 0 0 0 _/- PV (present value, negative because you're paying it out)

6 I/Y (annual interest rate)

25 2nd [*P/Y] N (25 years)

CPT FV (compute future value, see 66,974.55)

If the interest is compounded annually:

2nd [CLR TVM] (clear any existing results)

1 5 0 0 0 _/- PV (present value, negative because you're paying it out)

6 I/Y (annual interest rate)

2nd [P/Y] 1 ENTER 2nd [QUIT] (one compounding period per year)

25 N (25 years)

CPT FV (compute future value, see 64,378.96)

2nd [CLR TVM] (clear any existing results)

1 5 0 0 0 _/- PV (present value, negative because you're paying it out)

6 I/Y (annual interest rate)

25 2nd [*P/Y] N (25 years)

CPT FV (compute future value, see 66,974.55)

If the interest is compounded annually:

2nd [CLR TVM] (clear any existing results)

1 5 0 0 0 _/- PV (present value, negative because you're paying it out)

6 I/Y (annual interest rate)

2nd [P/Y] 1 ENTER 2nd [QUIT] (one compounding period per year)

25 N (25 years)

CPT FV (compute future value, see 64,378.96)

Oct 26, 2010 | Texas Instruments BA-II Plus Calculator

2 0 0 0 0 +/- PV (present value, negative because you're paying it out)

5 *P/YR (5 years)

1 0 . 5 I/YR (interest rate)

FV (calculate future value, about 33,732)

5 *P/YR (5 years)

1 0 . 5 I/YR (interest rate)

FV (calculate future value, about 33,732)

Aug 09, 2010 | HP 10bII Calculator

That depends on the interest rate.

2nd [CLR TVM] (clear previous data)

5 0 0 0 PMT (monthly payment)

2 0 2nd [*P/Y] N (20 years of monthly payments)

annual interest rate I/Y (annual interest rate)

CPT PV (compute present value)

At 10% it's about $518,000

2nd [CLR TVM] (clear previous data)

5 0 0 0 PMT (monthly payment)

2 0 2nd [*P/Y] N (20 years of monthly payments)

annual interest rate I/Y (annual interest rate)

CPT PV (compute present value)

At 10% it's about $518,000

May 26, 2010 | Texas Instruments BA-II Plus Calculator

The formula for population growth is:

population * (annual growth rate ^ number of years)

In your example,

6000000000 * (1.01^24) = 7618407891

To get your calculator to perfom the calculation, enter it in the following steps:

Type 6000000000

Press the multiply key

Press the ( key

Type 1.01

Press the yx key (located right above the divide key)

Type 24

Press the ) key

Press the = key

You can reuse this formula, substituting any values you wish for the current population, growth rate, and number of years.

Regards,

Javabytes

population * (annual growth rate ^ number of years)

In your example,

6000000000 * (1.01^24) = 7618407891

To get your calculator to perfom the calculation, enter it in the following steps:

Type 6000000000

Press the multiply key

Press the ( key

Type 1.01

Press the yx key (located right above the divide key)

Type 24

Press the ) key

Press the = key

You can reuse this formula, substituting any values you wish for the current population, growth rate, and number of years.

Regards,

Javabytes

Oct 29, 2007 | Texas Instruments TI-30XA Calculator

Feb 12, 2015 | HP 10bII Calculator

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