Chapter 1. calc_tutorial_5_8_037

1.1 Problem Statement

{10,11,12,13,14,15,16,17,18,19,20}
1000*$q
{4,5,6}
$t-2
$r/100
$t*$s
$t*$r
$p*$s
$p*$t/100
2.718281828
round($p/pow($e,$u),2)

How much must one invest today in order to receive $$p after $t years if interest is compounded continuously at the rate r = $r%?

1.2 Step 1

If P0 dollars are deposited into an account earning interest at an annual rate r compounded continuously, then the value of the account after t years is .

Question Sequence

Question 1.1

The desired value of the account after $t years is $$p, or P($t) = 3jRAm4T6Mr4=.

Interest is compounded continuously at a rate of $r%, so we let r = R7MvkioXBvw= .

Using , express P($t) in terms of P0.

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
Correct.
Incorrect.

1.3 Step 2

Since P($t) = $p, we have $p = P0e$u.

Question Sequence

Question 1.2

Solve for P0 rounded to the nearest cent.

$p = P0e$u.

P0 ≈ $qjqZz1N+poo=

Incorrect. Do you see where you went wrong?
Excellent work.