Tom's stockbroker offers an investment that is compounded continuously at an annual interest rate of 3.7%. If Tom wants a return of $25,000, how long will Tom's investment need to be if he puts $8000 initially? Give the exact solution in symbolic form and then estimate the answer to the tenth of a year.

It'll take 38.3 years to obtain the desired return of $25,000.

Step-by-step explanation:

In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:

M = C*e^(r*t)

Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:

(25000 + 8000) = 8000*e^(0.037*t)

33000 = 8000*e^(0.037*t)

e^(0.037*t) = 33000/8000

e^(0.037*t) = 4.125

ln[e^(0.037*t)] = ln(4.125)

t = ln(4.125)/(0.037)

t = 1.4171/0.037 = 38.2991

t = 38.3 years

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct