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3 years ago

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Charles owes $2,500 on a credit card. The card charges 12% interest compounded continuously. Write a formula that describes how

much Charles will owe on his card after t years assuming that he makes no payments that does not occur in any additional charges.

1 answer:

ella [17]3 years ago

4 0

Answer:

see below

Step-by-step explanation:

The formula for the amount resulting from P earning interest at rate r continuously compounded is ...

A = Pe^(rt)

for P=2500 and r=0.12, this becomes ...

A = 2500e^(0.12t)

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3 years ago

Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1

alexandr1967 [171]

Answer:

$a) \simeq 0.3012$ $b) \simeq 0.0494$ c) $\simeq 0.2438$

Step-by-step explanation:

Rate of collision,

1.2 collisions every 4 months

or, $\frac{1.2}{4}$

= 0.3 collisions per month

So, the Poisson distribution for the random variable no. of collisions per month (X) is given by,

P(X =x) = $\frac{e^{-\lambda}\times {\lambda}^{x}}}{x!}
$

for x ∈ N ∪ {0}

= 0 otherwise --------------------------------------(1)

here, $\lambda = 0.3$ collision / month

No collision over a 4 month period means no collision per month or X =0

Putting X = 0 in (1) we get,

P(X = 0) = $\frac{e^{-0.3}\times {\0.3}^{0}}{0!}
$

$\simeq 0.7408182207$ ------------------------------------(2)

Now, since we are calculating this for 4 months,

so, P(No collision in 4 month period)

= $0.7408182207^{4}$

$\simeq 0.3012$ -----------------------------------------------------------(3)

2 collision in 2 month period means 1 collision per month or X =1

Putting X =1 in (1) we get,

P(X =1) = $\frac{e^{-0.3}\times {\0.3}^{1}}{1!}
$

$\simeq 0.2222454662$ ------------------------------------(4)

Now, since we are calculating this for 2 months, so ,

P(2 collisions in 2 month period)

= $0.2222454662^{2}$

$\simeq 0.0494$ -----------------------------------------(5)

1 collision in 6 months period means

$\frac{1}{6}$ collision per month

Now, P(1 collision in 6 months period)

= P( X = 1/6] (which is to be estimated)

= $\frac {P(X=0)\times 5 + P(X =1)\times 1}{6}$

= \frac {0.7408182207 \times 5 + 0.2222454662 \times 1}{6}[/tex]

$\simeq 0.6543894283$ -------------------------------------------(6)

So,

P(1 collision in 6 month period)

= $0.6543894283^{6}$

$\simeq 0.0785267444$ ------------------------------------------------(7)

So,

P(No collision in 6 months period)

= $(P(X =0)^{6}$

$\simeq 0.1652988882$ ---------------------------------(8)

so,

P(1 or fewer collision in 6 months period)

= (8) + (7 ) = 0.0785267444 +0.1652988882

$\simeq 0.2438$ ---------------------------------------------(9)

7 0

2 years ago

What does y equal y-16-3y=0

Afina-wow [57]

Answer:

y = - 8

Step-by-step explanation:

y - 16 - 3y = 0

Group like terms

y - 3y - 16 = 0

Add similar elements: y - 3y = - 2y

- 2y - 16 = 0

Add 16 to both sides

- 2y - 16 + 16 = 0 + 16

Simplify

- 2y = 16

Divide both sides by - 2

$\frac{-2y}{-2}$ = $\frac{16}{-2}$

Simplify $\frac{-2y}{-2}$ : y

$\frac{-2y}{-2}$

Apply the fraction rule: $\frac{-a}{-b} = \frac{a}{b}$

= $\frac{2y}{2}$

Divide the numbers: $\frac{2}{2} = 1$

= y

Simplify $\frac{16}{-2}$ : - 8

$\frac{16}{-2}$

Apply the fraction rule: $\frac{-a}{-b} = \frac{a}{b}$

$-\frac{16}{2}$

Divide the numbers: $\frac{16}{2}$ = 8

= - 8

y = - 8

7 0

3 years ago