compound interest

b_austintx · #1 $Old$ April 26th, 2009, 10:17 PM

ok i have two questions that i need help on. ugh word problems...

1. a car tire has a small leak, and the tire pressure in pounds per square inch after t minutes is given by

P(t) = 32e (-0.2t) After how many minutes was the pressure 5 pounds per square inch?

*note the (-0.2t) is the exponent.

there is not time- so i'm not sure what to plug into (t)? plug in (60) for (t) since its talking about minutes?? and since its neg. i keep getting a neg. answer. but there is no such thing as a neg min. so i'm stuck....

2. Suppose $8000 is invested into a savings account that accrues intrest continuously at a rate of 2.3% determine how long it would take the investment to triple.

its continuously...there is no year or quartly so how do i solve?
i think the formula to use is

A=P (1 + r/t) ^ nt -----is this right?

what do i do for t? apparently time that i have the problem with in both questions.

can anyone help?

SengNee · #2 $Old$ April 26th, 2009, 11:40 PM

Quote:

Originally Posted by b_austintx $View Post$

ok i have two questions that i need help on. ugh word problems...

1. a car tire has a small leak, and the tire pressure in pounds per square inch after t minutes is given by

P(t) = 32e (-0.2t) After how many minutes was the pressure 5 pounds per square inch?

*note the (-0.2t) is the exponent.

there is not time- so i'm not sure what to plug into (t)? plug in (60) for (t) since its talking about minutes?? and since its neg. i keep getting a neg. answer. but there is no such thing as a neg min. so i'm stuck....

2. Suppose $8000 is invested into a savings account that accrues intrest continuously at a rate of 2.3% determine how long it would take the investment to triple.

its continuously...there is no year or quartly so how do i solve?
i think the formula to use is

A=P (1 + r/t) ^ nt -----is this right?

what do i do for t? apparently time that i have the problem with in both questions.

can anyone help?

1)
Given, $P(t)=5$
$32e^{-0.2t}=5$

2)
After 1st year, $T_1=8000(1.023)$ .
After 2nd year, $T_2=8000(1.023)(1.023)$ .
After 3rd year, $T_3=8000(1.023)(1.023)(1.023)$ .

It is a G.P.

$a=8000$
$r=1.023$

$T_1=ar$
$T_2=ar^2$
$T_3=ar^3$

Given, after $n^{th}$ year, the investment is tripled.

Therefore, $T_n=3a$

b_austintx · #3 $Old$ April 27th, 2009, 12:05 AM

1). i'm still lost. i get that p(t)= 5
but what about the -0.2t ? do i place the 5 in and multiply?

which if i did i would get 32e^{-0.2t} =86.98
? 86.98 = 5 ?

what are the steps for this problem?

2.)

so after the 3rd year the investment tripled?

i just take a=8000 and mult. that by 3??

what do you mean it is a G.P? there wasn't a formula that i needed to use?