Help math problem!!?

I use this equation for exponential decay problems:

A(t) = a₀ e^(kt)

Where a₀ is the initial amount,

A(t) is the amount after time "t"

k is the decay constant.

If we're checking for half-life, we can set a₀ = 1, A(t) = 0.5, and t = 1690.  Now we can solve for k:

A(t) = a₀ e^(kt)

0.5 = 1 e^(k * 1690)

0.5 = e^(1690k)

ln(0.5) = 1690k

k = ln(0.5) / 1690

Which is approx:

k = -0.00041015 (rounded to 5SF)

So now our equation is:

A(t) = a₀ e^(-0.00041015t)

If we say that a₀ = 90, then want to see how much is left after 450 years, solve for A(450):

A(t) = 90 e^(-0.00041015t)

A(450) = 90 e^(-0.00041015 * 450)

A(450) = 90 e^(-0.1845675)

A(450) = 90(0.83146)

A(450) = 74.832 g (rounded to 3DP)

The decay factor is 0.5^(t/1690) where t is in years.

You see, the amount is cut in half for each multiple of 1690.

So plug in 450 for t, calculate the factor, and multiply by 90.

M = 90*(1/2)^(t/1690)

t=450--->M=74.8 g