Lesson 5-3

Exponential Functions

Exponential Functions:

Any function in of the form of: f(x) = abx

where a>0, and b>0 and b≠1.

Exponential Functions:

Parent graphs for the general exponential functions are:

Parent graphs for the general exponential functions are:

Parent graphs for the general exponential functions are:

b > 1

Parent graphs for the general exponential functions are:

Parent graphs for the general exponential functions are:

0 < b < 1

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

f(0) = 3 (0,3) 3 = ab0 3 = a

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

f(0) = 3 (0,3) 3 = ab0 3 = a

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

f(0) = 3 (0,3) 3 = ab0 3 = a

f(2) = 12 (2,12) 12 = (3)b2 4 = b2 + 2 = b

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

f(0) = 3 (0,3) 3 = ab0 3 = a

f(2) = 12 (2,12) 12 = (3)b2 4 = b2 + 2 = b

(b must be positive so b = 2.)

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

Therefore, our function is f(x) = 3(2)x.

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

Therefore, our function is f(x) = 3(2)x.

Thus, f(-2) = 3(2)-2.

If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

Use the general format: f(x) = abx

Therefore, our function is f(x) = 3(2)x.

Thus, f(-2) = 3(2)-2.

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

f(t) = abt

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

f(t) = abt but we just worked with this as

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

f(t) = abt but we just worked with this as

A(t) = A0(1 + r)t

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

so, we now adjust and get

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

so, we now adjust and get

A(t) = A0b(t/k)

When exponential functions are used to represent exponential growth and decay, the

variable t is used to represent time. Our functions can easily be written as:

so, we now adjust and get

A(t) = A0b(t/k)

(k = time needed to multiply A0 by b)

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

A(t) = A0(2t/12)

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

A(t) = A0(2t/12)

To express A(t) in form (1), reason as follows.

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

A(t) = A0(2t/12)

To express A(t) in form (1), reason as follows.

A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

A(t) = A0(2t/12)

To express A(t) in form (1), reason as follows.

Rule of 72: If a quantity is growing at r% per year

(or month) then the doubling time is approximately 72 / r years (or months).

For example, if a quantity grows at a rate of 8% per year then the quantity will double in

approximately (72 / 8) or 9 years. If a population is growing exponentially at a

rate of 2% per month then the population will double in about (72 / 2) or 36 months.

A radioactive isotope has a half-life of 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day?

A radioactive isotope has a half-life of 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day?

A radioactive isotope has a half-life of 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day?

So, the daily rate of decay is 13%.

Assignment:

Pgs. 183-184C.E. 1-10 all,W.E. 1-11 odd