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Solve the problem. A box contains a radioactive substance.  The number of kilograms, r(t), at time t years is given by r(t) = 2-0.002588t.  How long will it take until only one-half kilogram of the radioactive substance is left in the box?

Solve the problem.At what interest rate would a deposit of $50,000 grow to $ 116,982 in 25 years with continuous compounding?

Solve the equation for x by first rewriting both sides as powers of the same base.

Convert to a logarithmic equation. 

Convert to an exponential equation.log381 = 4

If $ 2000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 2800 at 8.25%?

Solve the problem.An initial investment of $1000 is appreciated for 5 years in an account that earns 12% interest, compounded annually. Find the amount of money in the account at the end of the period.

Solve the logarithmic equation.log(x – 3) = 1 – log x

Write the expression in expanded form. ln[x(x – 1)]

Solve the problem.An initial investment of $480 is appreciated for 7 years in an account that earns 15% interest, compounded quarterly. Find the amount of money in the account at the end of the period.