So far we have worked with rational bases for exponential functions. For most real-world phenomena, however,
e is used as the base for exponential functions. Exponential models that use
as the base are called
continuous growth or decay models . We see these models in finance, computer science, and most of the sciences, such as physics, toxicology, and fluid dynamics.
The continuous growth/decay formula
For all real numbers
and all positive numbers
and
continuous growth or decay is represented by the formula
where
is the initial value,
is the continuous growth rate per unit time,
and
is the elapsed time.
If
, then the formula represents continuous growth. If
, then the formula represents continuous decay.
For business applications, the continuous growth formula is called the continuous compounding formula and takes the form
where
is the principal or the initial invested,
is the growth or interest rate per unit time,
and
is the period or term of the investment.
Given the initial value, rate of growth or decay, and time
solve a continuous growth or decay function.
Use the information in the problem to determine
, the initial value of the function.
Use the information in the problem to determine the growth rate
If the problem refers to continuous growth, then
If the problem refers to continuous decay, then
Use the information in the problem to determine the time
Substitute the given information into the continuous growth formula and solve for
Calculating continuous growth
A person invested $1,000 in an account earning a nominal 10% per year compounded continuously. How much was in the account at the end of one year?
Since the account is growing in value, this is a continuous compounding problem with growth rate
The initial investment was $1,000, so
We use the continuous compounding formula to find the value after
year:
Radon-222 decays at a continuous rate of 17.3% per day. How much will 100 mg of Radon-222 decay to in 3 days?
Since the substance is decaying, the rate,
, is negative. So,
The initial amount of radon-222 was
mg, so
We use the continuous decay formula to find the value after
days:
Using the data in
[link] , how much radon-222 will remain after one year?
3.77E-26 (This is calculator notation for the number written as
in scientific notation. While the output of an exponential function is never zero, this number is so close to zero that for all practical purposes we can accept zero as the answer.)
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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