math word problems

Question

(1) There was a sample of 650 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 6.7% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.Write an exponential function showing the relationship between y and t. 

(2) Ryan deposited $4000 into an account with 4.7% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 4 years?Do not round any intermediate computations, and round your answer to the nearest cent. 

Answer 1

1. So, if something decays by 6.7%, we're left with 93.3%, right? Each year, the total is 93.3% of the year before. After 1 year, we have 93.3%, after year 2, we have 93.3% of that 93.3%, and so on.

y = 650(0.933)^t

2. If we have growth of 4.7%, each year's total is 104.7% of the year before.

4000(1.047)⁴ = $4806.70

Answer 2

Question 1: The general exponential equation for decay is given as:

N=N₀e^-rt

N₀ : the initial quantity

r: rate of decay

t: time

So with this information we need to first convert the rate that was given in percent to decimal, so 6.7% will become 0.067. Now we can replace the equation above to:

Answer:

y = 650e^-0.067t

Question 2:

Compound interest equation:

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

A: total new amount

P: initial amount

r: interest rate

n: how much compounded

t: time

now we can substitute everything given the information in the question to:

A = 4000(1+0.047/2)²⁽⁴⁾

A = 4816.846063

Nearest cent: 4816.85

Hope this helps, if you have any other questions you can message me directly, always here to help.