Goal: Use our calculator to solve simple exponential equations such as
.
EX: Use your calculator to solve the following:
1)
(
2)
)
(
3)
)
(
4)
)
(
(
)
)
(
)
Many calculators cannot evaluate logs with bases with bases other than 10 and e.
Change of Base formula:
EX: Calculate the following using the change of base formula
(
( )
( )
( )
(
)
( )
( )
)
EX: Use your calculator to solve the following exponential equations.
1)
( )
( )
( )
You can check this….do
2)
(
(
)
)
( )
. We get 50.040 which is pretty close (rounding)
3)
(
You can check this….do
. We get 901.18 which is pretty close (rounding)
You can check this….do
. We get 12.001 which is pretty close (rounding)
)
( )
( )
4)
No need for change of base (make sure to pay attention)
( )
(
)
5)
You can check this….do
. We get 45.015 which is pretty close (rounding)
You can check this….do
. We get 8.004 which is pretty close (rounding)
You can check this….do
. We get 0.4997 which is pretty close (rounding)
You can check this….do
. We get 19.987 which is pretty close (rounding)
( )
( )
( )
6)
( )
( ⁄ )
( )
7)
(
(
(
8)
)
)
)
(
)
( )
( )
DUH! We knew
already! We didn’t need a calculator for this.
9)
(
(
(
)
)
)
You can check this….do
(rounding)
. We get 25.003 which is pretty close
EX: A population of insects is introduced to a breeding enclosure. The population is given by the
function ( )
where t is measured in days.
How many days will it take for the insect population to be 150?
I know the population needs to be 150, so I’ll solve for
(
)
(
(
)
)
In about 27.5 days there will be 150 insects in the enclosure.
EX: A one ton sand dune is slowly being washed away by the ocean. It amount of sand (S measured in
tons) is given by the function ( )
where t is measured in weeks.
How many weeks will it take for there to be only half a ton of sand?
I know the sand needs to be 0.5, so I’ll solve for
( )
Keep in mind this is negative t….I’ll take care of that later.
(
(
If
)
)
that means that
In about 23.1 weeks there will be half a ton of sand in the dune.