Nancy wants to invest dollar 4000 in saving certificates tha

Nancy wants to invest dollar 4000 in saving certificates that bear an interest rate of 9.75% per year, compounded semiannually. How long a time period should she choose to save an amount of dollar 5000? Suppose you\'re driving your car on a cold winter day (20degree F) and the engine overheats. When you park, the engine begins to cool down. The temperature T of the engine t minutes after you park satisfies the equation In = -0.11t. Find the temperature of the engine after 20 minutes?

Solution

9 ) amount invested = $ 4000

rate of interest = 9.75% compounded semiannually

applying compound interest formula

A = P ( 1+r/n)^nt

n =2 for semiannully compounding

5000 = 4000 ( 1+ .0975 / 2 ) ^2t

dividing both sides bu 4000

1.25 = ( 1.04875)^2t

applying log on both sides

ln 1.25 = 2t ln ( 1.04875 )

2t = 4.6879

t = 2.34

after approximately 2.34 years amount would be $ 5000

10) ln {( T -20 ) / 200} =-.11t

temperature of engine after 20 minutes

plug t = 20

ln { ( T - 20 ) / 200} = -.11(20)

ln { ( T - 20 ) / 200} = -2.2

{ ( T - 20 ) / 200} = e^-2.2

( T - 20 ) / 200} = .11080

T = 42.16

temperature is 42.16 degress F