Exponential Growth Problem. Is this solution correct?
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I would just like to confirm that I'm doing this correctly. If not, any help would be appreciated. Thanks!
The problem:
A painting sold for $$274$ in $1977$ and was sold again in $1987$ for $$470$. Assume that the growth in the value $V$ of the collector’s item was exponential.
Find the value $k$ of the exponential growth rate. Assume $V_0 = 274$.
My attempt at solving it:
$470=274e^{10k}$
$k = 0.054$ (rounded to the nearest thousandth)
algebra-precalculus proof-verification exponential-function
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
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add a comment |
$begingroup$
I would just like to confirm that I'm doing this correctly. If not, any help would be appreciated. Thanks!
The problem:
A painting sold for $$274$ in $1977$ and was sold again in $1987$ for $$470$. Assume that the growth in the value $V$ of the collector’s item was exponential.
Find the value $k$ of the exponential growth rate. Assume $V_0 = 274$.
My attempt at solving it:
$470=274e^{10k}$
$k = 0.054$ (rounded to the nearest thousandth)
algebra-precalculus proof-verification exponential-function
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
$endgroup$
$begingroup$
The answer is correct.
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– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07
add a comment |
$begingroup$
I would just like to confirm that I'm doing this correctly. If not, any help would be appreciated. Thanks!
The problem:
A painting sold for $$274$ in $1977$ and was sold again in $1987$ for $$470$. Assume that the growth in the value $V$ of the collector’s item was exponential.
Find the value $k$ of the exponential growth rate. Assume $V_0 = 274$.
My attempt at solving it:
$470=274e^{10k}$
$k = 0.054$ (rounded to the nearest thousandth)
algebra-precalculus proof-verification exponential-function
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
$endgroup$
I would just like to confirm that I'm doing this correctly. If not, any help would be appreciated. Thanks!
The problem:
A painting sold for $$274$ in $1977$ and was sold again in $1987$ for $$470$. Assume that the growth in the value $V$ of the collector’s item was exponential.
Find the value $k$ of the exponential growth rate. Assume $V_0 = 274$.
My attempt at solving it:
$470=274e^{10k}$
$k = 0.054$ (rounded to the nearest thousandth)
algebra-precalculus proof-verification exponential-function
algebra-precalculus proof-verification exponential-function
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
edited Feb 4 '18 at 10:43
TheSimpliFire
13k62464
13k62464
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
asked Mar 7 '14 at 21:53
LearnerLearner
35941022
35941022
$begingroup$
The answer is correct.
$endgroup$
– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07
add a comment |
$begingroup$
The answer is correct.
$endgroup$
– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07
$begingroup$
The answer is correct.
$endgroup$
– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
The answer is correct.
$endgroup$
– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07
add a comment |
1 Answer
1
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Your answer is correct. The exact value would be
$$k = frac{1}{10}ln{left(frac{470}{274}right)}$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
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add a comment |
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1 Answer
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active
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votes
1 Answer
1
active
oldest
votes
active
oldest
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active
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votes
$begingroup$
Your answer is correct. The exact value would be
$$k = frac{1}{10}ln{left(frac{470}{274}right)}$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
$endgroup$
add a comment |
$begingroup$
Your answer is correct. The exact value would be
$$k = frac{1}{10}ln{left(frac{470}{274}right)}$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
$endgroup$
add a comment |
$begingroup$
Your answer is correct. The exact value would be
$$k = frac{1}{10}ln{left(frac{470}{274}right)}$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
$endgroup$
Your answer is correct. The exact value would be
$$k = frac{1}{10}ln{left(frac{470}{274}right)}$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
answered Mar 14 '14 at 9:42
naslundxnaslundx
7,98352941
7,98352941
add a comment |
add a comment |
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$begingroup$
The answer is correct.
$endgroup$
– André Nicolas
Mar 7 '14 at 21:56
$begingroup$
Correct, but you might want to write the exponent as $10k$.
$endgroup$
– marty cohen
Jul 24 '17 at 22:07