Developing Expert Voices Question 1 pt 2

1. Question # 1
Part 2

2. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
(b) How long will it take her to collect 90 different gowns?

3. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
(b) How long will it take her to collect 90 different gowns?
What formula can we use? Her closet is exponentially growing continuously, with
that given we can use the continual compound interest equation.

4. Serena now has 2 gowns but after getting her dress done she gets
hooked to gowns. She keeps on buying and buying gowns. She bought
so many gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
(b) How long will it take her to collect 90 different gowns?
What formula can we use? Her closet is exponentially growing continuously, with
that given we can use the continual compound interest equation.
r t
A = Pe
Where: A is the amount after time(t)
P is the principle value (initial amount)
r is rate
t is time
e is just a irrational number whose value is 2.71828182845 . . .

5. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
r t
A = Pe
We are given the principle, rate and time. So we are solving for A.

6. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
r t
A = Pe
We are given the principle, rate and time. So we are solving for A.
A = ? Plug every thing you have into the equation and solve of A
P = 2
r = 8.4% = 0.084
t = 20 days

7. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
r t
A = Pe
We are given the principle, rate and time. So we are solving for A.
A = ? Plug every thing you have into the equation and solve of A
P = 2 (0.084)(20)
A = 2e
r = 8.4% = 0.084
t = 20 days

8. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
r t
A = Pe
We are given the principle, rate and time. So we are solving for A.
A = ? Plug every thing you have into the equation and solve of A
P = 2 (0.084)(20)
A = 2e
r = 8.4% = 0.084
t = 20 days Enter it into you calculator and . . . A = 10.73

9. Serena now has 2 gowns but after getting her dress done she gets hooked
to gowns. She keeps on buying and buying gowns. She bought so many
gowns that her closet exponentially grows at a rate of 8.4%
(a) How many different gowns will she have after 20 days?
r t
A = Pe
We are given the principle, rate and time. So we are solving for A.
A = ? Plug every thing you have into the equation and solve of A
P = 2 (0.084)(20)
A = 2e
r = 8.4% = 0.084
t = 20 days Enter it into you calculator and . . . A = 10.73
After 20 days she will have 11 gowns.
We round it up since she can't have .73 of a gown.

10. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t
A = Pe
A = 90
P = 2
r = 8.4 % = 0.084
t = ?

11. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90
P = 2
r = 8.4 % = 0.084
t = ?

12. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90 Divide out the 2 on both
(0.084)(t) side of the equation to
P = 2 90 = 2e make it nicer and easier
r = 8.4 % = 0.084 2 2 to work with.
t = ?

13. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90 Divide out the 2 on both
(0.084)(t) side of the equation to
P = 2 90 = 2e make it nicer and easier
r = 8.4 % = 0.084 2 2 to work with.
t = ?
Lets take the natural logarithm of the equation.
ln 45 = 0.084)(t) lne
( lne = 1

14. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90 Divide out the 2 on both
(0.084)(t) side of the equation to
P = 2 90 = 2e make it nicer and easier
r = 8.4 % = 0.084 2 2 to work with.
t = ?
Lets take the natural logarithm of the equation.
ln 45 = 0.084)(t) lne
( lne = 1
ln 45 = (0.084)(t)(1)
Solve for t
ln 45 = t
0.084

15. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90 Divide out the 2 on both
(0.084)(t) side of the equation to
P = 2 90 = 2e make it nicer and easier
r = 8.4 % = 0.084 2 2 to work with.
t = ?
Lets take the natural logarithm of the equation.
ln 45 = 0.084)(t) lne
( lne = 1
ln 45 = (0.084)(t)(1)
Solve for t
ln 45 = t
0.084
t= 45.3174 . . .

16. (b) How long will it take her to collect 90 different gowns?
We are still using the continual compound interest formula. Since her wardrobe is still compounding
continuously but this time we are given A and are solving for time(t)
r t (0.084)(t)
A = Pe 90 = 2e
How do we bring the t down? hmmmm. . . .
A = 90 Divide out the 2 on both
(0.084)(t) side of the equation to
P = 2 90 = 2e make it nicer and easier
r = 8.4 % = 0.084 2 2 to work with.
t = ?
Lets take the natural logarithm of the equation.
ln 45 = 0.084)(t) lne
( lne = 1
ln 45 = (0.084)(t)(1)
Solve for t
ln 45 = t
0.084
t= 45.3174 . . .
I will take Serena 45.32 days to
reach 90 different gowns.

17. Question # 1 solved!!

18. Attachments
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