Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 14:12
- Lesson: 27:21

We now have a better understanding of how the compounding frequency will affect the amount we wish to grow or decay. But what if we are dealing with something, say, that compounds every minute, second, or even millisecond? This concept is also known as continuous compounding. In this section, we will see a slight variation of an exponential growth and decay formula that models continuous exponential growth/decay.

Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

Continuous Growth/Decay: ${ A_f = A_i e^{rt}}$

${A_f}$: final amount

${A_i}$ : initial amount

${e }$ : constant = 2.718…

${r }$ : rate of growth/decay

• growth rate of 7% $\to {r = {7\over100} = 0.07}$

• growth rate of 15%$\to {r = - {15\over100} = - 0.15}$

${t }$ : total time given

${A_f}$: final amount

${A_i}$ : initial amount

${e }$ : constant = 2.718…

${r }$ : rate of growth/decay

• growth rate of 7% $\to {r = {7\over100} = 0.07}$

• growth rate of 15%$\to {r = - {15\over100} = - 0.15}$

${t }$ : total time given

- 1.On Aiden’s 10-year-old birthday, he deposited $20 in a savings account that

offered an interest rate of 4% compounded continuously. How much money

will Aiden have in the account when he retires at the age of 60? - 2.A radioactive substance decays continuously. If the half-life of the substance

is 5 years, determine the rate of decay.

19.

Exponential Functions

19.1

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

19.2

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

19.3

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

19.4

Exponents: Negative exponents

19.5

Exponents: Zero exponent: $a^0 = 1$

19.6

Exponents: Rational exponents

19.7

Graphing exponential functions

19.8

Graphing transformations of exponential functions

19.9

Finding an exponential function given its graph

19.10

Continuous growth and decay in exponential and logarithmic functions

We have over 1180 practice questions in Algebra 1 for you to master.

Get Started Now