Question

solve the problem.
a sample of 1000 g of lead - 210 decays to polonium - 210 according to the function given by ( a(t)=1000 e^{-0.032 t} ), where ( t ) is time in years. what is the amount of the sample after 40 years (to the nearest g)?
( 3597 mathrm{~g} )
( 202 mathrm{~g} )
( 278 mathrm{~g} )
( 16 mathrm{~g} )
question 4
0.1 pts
solve the problem.
the size of the beaver population at a national park increases at the rate of ( 4.9 % ) per year. if the size of the current population is 124, find how many beavers there should be in 6 years. use the function ( f(x)=124 e^{0.049 x} ) and round to the nearest whole number.
( 170 )
( 166 )
( 168 )
( 164 )

Explanation:

Step1: Substitute t=40 into A(t)

$A(40) = 1000e^{-0.032(40)}$

Step2: Calculate exponent

$-0.032×40 = -1.28$

Step3: Compute exponential value

$e^{-1.28} ≈ 0.278$

Step4: Find A(40)

$1000×0.278 = 278$

Step1: Substitute x=6 into f(x)

$f(6) = 124e^{0.049(6)}$

Step2: Calculate exponent

$0.049×6 = 0.294$

Step3: Compute exponential value

$e^{0.294} ≈ 1.342$

Step4: Find f(6)

$124×1.342 ≈ 166$

Answer:

278 g