1. ## compound interest

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? 2. Originally Posted by b_austintx 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, $\displaystyle P(t)=5$
$\displaystyle 32e^{-0.2t}=5$

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

It is a G.P.

$\displaystyle a=8000$
$\displaystyle r=1.023$

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

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

Therefore, $\displaystyle T_n=3a$

3. 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?