# The function #f(t)=Pe^(rt)# describes the amount #P# will become if invested for #t# years at #r%# per annum compounded continuously. If a sum becomes #$246.40# at #4%# in #4# years, what is the amount invested?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the amount invested (P), we can use the formula ( P = \frac{A}{e^{rt}} ), where A is the final amount, r is the interest rate (in decimal form), t is the time in years, and e is the base of the natural logarithm (approximately equal to 2.71828).

Given: A = $246.40 r = 4% = 0.04 (in decimal) t = 4 years

Using the given values in the formula, we get: [ P = \frac{246.40}{e^{0.04 \times 4}} ]

[ P \approx \frac{246.40}{e^{0.16}} ]

[ P \approx \frac{246.40}{1.1735} ]

[ P \approx 209.88 ]

So, the amount invested is approximately $209.88.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the amount invested, we can use the formula for continuous compounding: ( P = \frac{A}{e^{rt}} ), where ( P ) is the initial principal, ( A ) is the final amount, ( r ) is the interest rate, and ( t ) is the time in years.

Given: ( A = 246.40 ) ( r = 0.04 ) (4% expressed as a decimal) ( t = 4 )

We can rearrange the formula to solve for ( P ): ( P = \frac{A}{e^{rt}} )

Substituting the given values: ( P = \frac{246.40}{e^{0.04*4}} )

Now, calculate: ( P = \frac{246.40}{e^{0.16}} )

Using the approximate value of ( e ) (2.71828): ( P = \frac{246.40}{2.71828^{0.16}} )

Calculate ( e^{0.16} ): ( e^{0.16} ≈ 1.17351087 )

Now divide: ( P ≈ \frac{246.40}{1.17351087} )

( P ≈ 210.00 )

So, the amount invested is approximately $210.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7