Thread: HELP! please. very urgent. precal.

ok here are some questions i need help with ASAP.

1)express this using rational exponents: 5 times the square root of 81x^(3)y^(8) (theres also a little 4 above the beginning of the radical.)



2)a scientist has 37 grams of a radioactive substance that decays exponentially. assuming k= -0.3, how many grams of radioactive substance remain after 9 days? round your answer to the nearest hundredth.

3) solve using common logarithms: 4^(x-3)=7^x



4)what interest rate is required for an investment with continuously compounded interest to double in 8 years?

Originally Posted by taylorr556

ok here are some questions i need help with ASAP.

1)express this using rational exponents: 5 times the square root of 81x^(3)y^(8) (theres also a little 4 above the beginning of the radical.)

Hint:

see post #3 here to see how to change radicals to powers.

now what do you think we should do?

2)a scientist has 37 grams of a radioactive substance that decays exponentially. assuming k= -0.3, how many grams of radioactive substance remain after 9 days? round your answer to the nearest hundredth.

the general equation for a problem like this is:

(the power should be negative for decay, in general we consider r or in this case, k, to be positive)

here, is the amount remaining after time t, is the initial amount, (or ) is the rate of decay, and t is time.

given the information in your question, our equation for this particular problem is:



you want , now continue

3) solve using common logarithms: 4^(x-3)=7^x

take log to the base 10 of both sides:



.........since

now we simply solve for , i leave that to you

4)what interest rate is required for an investment with continuously compounded interest to double in 8 years?

the equation we use for continuous compounding is the same one we use for exponential growth. the time it takes to double is 8 years, so we know the interest rate is .

we could have solved for this by solving for . but this formula works in general. that is when is the half-life (in the case of radioactive decay) or is the doubling time (in the case of exponential growth)