Exercise 56 Page 339

Since the interest is compounded monthly, we have to use a formula that describes compound interest. y=a(1+r/n)^(nt) In this function, a is the initial amount, r is the percent increase expressed in decimal form, t is the time in years and n is the number of times the initial principal is compounded per year. From the exercise, we know that a=1000, r= 0.035 and n= 12 since the interest is compounded monthly. y=1000(1+0.035/12)^(12t)We want to know the value of t when y is greater than or equal to 1200. Let's first simplify as much as possible and isolate the term with the variable in the exponent.

Now that the term with the variable in the exponent has been isolated, we can take the logarithm of both sides.

After about 5.22 months the balance is at least $1200. Let's also determine when the balance is at least $3500.

Now that the term with the variable in the exponent has been isolated, we can take the logarithm of both sides.

After about 35.85 months the balance is at least $3500.