Question

A radioactive substance decays at a continuous rate of 12% per year, and 90 mg of the substance is present in the year 2000. (a) Write a formula for the amount present, A (in mg), t years after 2000. MathPAD Response msnViewer_resp_str_c04q_go_2_006_1_svg ViewEdit (b) How much will be present in the year 2010

Answer 1

A(t) = 90e^0.12t ;

299 mg

Explanation:

General Continous growth rate equation :

A = Pe^rt

A = amount present, t years after year of initial amount.

Here,

P = 90 mg, amount in year 2000

r = rate = 12% = 0.12

t = years after 2000

Therefore,

A is written as ;

A(t) = 90e^0.12t

Amount present in year 2010 ;

t = 2010 - 2000 = 10

A(10) = 90e^0.12(10)

A(10) = 90 * e^1.2

= 90 * 3.3201169

= 298.81052

= 299 mg