PRACTISING The formula to calculate the mass, M(u). sample of radioactive materi

Question

PRACTISING The formula to calculate the mass, M(u). sample of radioactive material with mass is formula M P(!) P, determ substance. where t time and h is the h The is it take half-life of a radioactive substance is 8 a) for a 300 g sample to decay to each mass? 200 g b) 100 g 75 g 5, Solve. 1296 b) 2 0.25 e) 2 2 7 71 81 (27) If $500 is deposited into an account that pays 8% annually, how long will it take for the deposit to do b) A $1000 investment is made in a trust fund that pay compounded monthly. How long will it take the in grow to S5000? A S5000 investment is made in a savings account th compounded quarterly. How long will it take for th to grow to $7500? an account that pays 12%/a

Explanation / Answer

5

a)

49^x-1 = 7sqrt(7)
7^2x-2 = 7^3/2
2x-2 = 3/2
2x = 7/2
x = 7/4

d)

36^2x+4 = 6^2x
6^(4x+8) = 6^2x
4x+8 = 2x
2x=-8
x=-4

b)

2^3x-4 = .25 = 2^-2
3x-4 = -2
3x = 2
x=2/3

e)

2^2x+2 +7 = 71
2^2x+2 = 64
2^2x+2 = 2^6
2x+2 = 6
x=2

c)

(1/4)^x+4 = sqrt(8)
-2x-8 = 3/2
-4x-16 = 3
4x = -19
x=019/4

f)

9^2x+1 = 81(27^x)
9^2x+1 = 9^2 *9^3x
2x+1 = 2+3x
-x = 1
x=-1

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