Math 1425.P70
Test 3
Name _________________________________________________
Differentiate.
1) f(x) = 5e-3x
Find the indicated tangent line.
2) Find the tangent line to the graph of f(x) = e6x at the point (0, 1).
Test 3
Solve the problem.
3) Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by
A(t) = 760e-0.23t. Find the rate of change of the quantity present at the time when t = 4.
Find the derivative of the function.
4) y = ln (8x3 - x2 )
Math 1425.P70 Test 3, page A-2
Solve the problem.
5) Find the doubling time for an amount invested at a growth rate 12% per year compounded continuously.
6) A radioactive substance has a decay rate of 3.5% per day. What is its half-life?
Math 1425.P70 Test 3, page A-3
Solve.
7) The initial weight of a starving animal is W0. Its weight after t days is given by
W = W0e-0.008t.
What percentage of its initial weight remains after 26 days?
Differentiate.
8) f(x) = x3 log7 x
Math 1425.P70 Test 3, page A-4
Find the elasticity.
9) q = D(x) = 300 - 4x
For the demand function given, find the elasticity at the given price and state whether the demand is elastic, inelastic, or
whether it has unit elasticity.
10) q = D(x) = 800 - 8x; x = 51
Math 1425.P70 Test 3, page A-5
BONUS
Solve.
11) In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It is found
that 16 g of A will reduce to 8 g in 2.9 hours. After how long will there be only 0.125 g left?
Math 1425.P70 Test 3, page A-6
Answer Key
Testname: TEST3
1) -15e-3x
2) y = 6x + 1
3) -69.7 grams per year
24x - 2
4)
8x 2 - x
5) 5.8 years
6) 19.8 days
7) 81.2%
x2
8)
+ 3x2 (log7 x)
ln 7
9) E(x) =
10)
x
75 - x
51
; elastic
49
11) 11.6 hours
Math 1425.P70 Test 3, page A-7
Math 1425.P70
Test 3
Name _________________________________________________
Differentiate.
1) f(x) = 7e-3x
Find the indicated tangent line.
2) Find the tangent line to the graph of f(x) = e8x at the point (0, 1).
Test 3
Solve the problem.
3) Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by
A(t) = 320e-0.58t. Find the rate of change of the quantity present at the time when t = 6.
Find the derivative of the function.
4) y = ln (3x3 - x2 )
Math 1425.P70 Test 3, page B-2
Solve the problem.
5) Find the doubling time for an amount invested at a growth rate 4% per year compounded continuously.
6) A radioactive substance has a decay rate of 6.9% per day. What is its half-life?
Math 1425.P70 Test 3, page B-3
Solve.
7) The initial weight of a starving animal is W0. Its weight after t days is given by
W = W0e-0.007t.
What percentage of its initial weight remains after 23 days?
Differentiate.
8) f(x) = x9 log6 x
Math 1425.P70 Test 3, page B-4
Find the elasticity.
9) q = D(x) = 300 - 2x
For the demand function given, find the elasticity at the given price and state whether the demand is elastic, inelastic, or
whether it has unit elasticity.
10) q = D(x) = 300 - 5x; x = 45
Math 1425.P70 Test 3, page B-5
BONUS
Solve.
11) In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It is found
that 8 g of A will reduce to 4 g in 4.9 hours. After how long will there be only 0.125 g left?
Math 1425.P70 Test 3, page B-6
Answer Key
Testname: TEST3
1) -21e-3x
2) y = 8x + 1
3) -5.7 grams per year
9x - 2
4)
3x 2 - x
5) 17.3 years
6) 10 days
7) 85.1%
x8
8)
+ 9x8 (log6 x)
ln 6
9) E(x) =
x
150 - x
10) 3; elastic
11) 14.7 hours
Math 1425.P70 Test 3, page B-7