Exercise 17 Page 461

We want to find the amount in a continuously compounded account for the given conditions. Principal:& $6000 Annual Interest Rate:& 6.8 % Time:& 10 yearsTo do so, we will start by recalling the formula for continuously compounded interest. A( t)= P * e^(r t) In this formula, A( t) represents the amount in the account at time t, P represents the initial value of the account or the principal, r is the annual interest rate, and t is the time in years. Let's substitute the given values into the formula. Note that r should be expressed as a decimal, so 6.8 %=0.068.

A(t)=P* e^(rt)

SubstituteValues

Substitute values

A(t)= 6000* e^(0.068( 10))

Multiply

Multiply

A(t)=6000* e^(0.68)

CalcPow

Calculate power

A(t)≈ 6000* 1.973877732

Multiply

Multiply

A(t)≈ 11843.27

The amount after 10 years under the given conditions is approximately $ 11843.27.