The future value that accrues when $500 is invested at 7%, compounded continuously, is s(t) = 500e0.07t where t is the number of years. (round your answers to the nearest cent.) (a) at what rate is the money in this account growing when t = 6? $ per year (b) at what rate is it growing when t = 12? $ per year

  (a) $53.27 per year

  (b) $81.07 per year

Step-by-step explanation:

The derivative of the function is ...

  S'(t) = 0.07·500e^(0.07t) = 35e^(0.07t)

(a) The derivative evaluated at t=6 is ...

  S'(6) = 35·e^0.42 ≈ 53.27

At t=6, the account is growing at the rate of $53.27 per year.

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(b) The derivative evaluated at t=12 is ...

  S'(12) = 35·e^0.84 ≈ 81.07

At t=12, the account is growing at the rate of $81.07 per year.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500