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 at 10:43
TheSimpliFire
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
add a comment |Â
up vote
0
down vote
favorite
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 at 10:43
TheSimpliFire
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 at 10:43
TheSimpliFire
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
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 at 10:43
TheSimpliFire
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
edited Feb 4 at 10:43
TheSimpliFire
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
edited Feb 4 at 10:43
TheSimpliFire
10.8k62054
edited Feb 4 at 10:43
TheSimpliFire
10.8k62054
edited Feb 4 at 10:43
TheSimpliFire
10.8k62054
10.8k62054
asked Mar 7 '14 at 21:53
Learner
3494921
asked Mar 7 '14 at 21:53
Learner
3494921
asked Mar 7 '14 at 21:53
Learner
3494921
3494921
The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07
add a comment |Â
The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07
The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07
add a comment |Â
1 Answer
1
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Your answer is correct. The exact value would be
$$k = frac110lnleft(frac470274right)$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundx
7,86052739
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Your answer is correct. The exact value would be
$$k = frac110lnleft(frac470274right)$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundx
7,86052739
add a comment |Â
up vote
0
down vote
Your answer is correct. The exact value would be
$$k = frac110lnleft(frac470274right)$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundx
7,86052739
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Your answer is correct. The exact value would be
$$k = frac110lnleft(frac470274right)$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundx
7,86052739
Your answer is correct. The exact value would be
$$k = frac110lnleft(frac470274right)$$
which approximates to: $k approx 0.054$ as you said. Well done.
answered Mar 14 '14 at 9:42
naslundx
7,86052739
answered Mar 14 '14 at 9:42
naslundx
7,86052739
answered Mar 14 '14 at 9:42
naslundx
7,86052739
answered Mar 14 '14 at 9:42
naslundx
7,86052739
7,86052739
add a comment |Â
add a comment |Â
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The answer is correct.
– André Nicolas
Mar 7 '14 at 21:56
Correct, but you might want to write the exponent as $10k$.
– marty cohen
Jul 24 '17 at 22:07