Expressing a curve function in a linear way
$begingroup$
Given the following function which expresses the relationship between $y$ and $t$ with constant factors $k$, $a$ and $b$:
$y=ke^{-frac{t}{ab}}$
Obtain another equation such that there is a linear relationship between $y$ and $t$.
I know that I need to obtain something of the form $y=mx+b$ and I don't even know if this is possible for other type of functions.
calculus linear-algebra
asked Dec 13 '18 at 18:58
margobra8margobra8
31
$endgroup$
add a comment |
$begingroup$
Given the following function which expresses the relationship between $y$ and $t$ with constant factors $k$, $a$ and $b$:
$y=ke^{-frac{t}{ab}}$
Obtain another equation such that there is a linear relationship between $y$ and $t$.
I know that I need to obtain something of the form $y=mx+b$ and I don't even know if this is possible for other type of functions.
calculus linear-algebra
asked Dec 13 '18 at 18:58
margobra8margobra8
31
$endgroup$
add a comment |
$begingroup$
Given the following function which expresses the relationship between $y$ and $t$ with constant factors $k$, $a$ and $b$:
$y=ke^{-frac{t}{ab}}$
Obtain another equation such that there is a linear relationship between $y$ and $t$.
I know that I need to obtain something of the form $y=mx+b$ and I don't even know if this is possible for other type of functions.
calculus linear-algebra
asked Dec 13 '18 at 18:58
margobra8margobra8
31
$endgroup$
Given the following function which expresses the relationship between $y$ and $t$ with constant factors $k$, $a$ and $b$:
$y=ke^{-frac{t}{ab}}$
Obtain another equation such that there is a linear relationship between $y$ and $t$.
I know that I need to obtain something of the form $y=mx+b$ and I don't even know if this is possible for other type of functions.
calculus linear-algebra
calculus linear-algebra
asked Dec 13 '18 at 18:58
margobra8margobra8
31
asked Dec 13 '18 at 18:58
margobra8margobra8
31
asked Dec 13 '18 at 18:58
margobra8margobra8
31
asked Dec 13 '18 at 18:58
margobra8margobra8
31
asked Dec 13 '18 at 18:58
margobra8margobra8
31
31
add a comment |
add a comment |
1 Answer
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$begingroup$
hint
for $t$ close to $a$,
$$f(t)approx f(a)+(t-a)f'(a)$$
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
$endgroup$
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
hint
for $t$ close to $a$,
$$f(t)approx f(a)+(t-a)f'(a)$$
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
$endgroup$
add a comment |
$begingroup$
hint
for $t$ close to $a$,
$$f(t)approx f(a)+(t-a)f'(a)$$
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
$endgroup$
add a comment |
$begingroup$
hint
for $t$ close to $a$,
$$f(t)approx f(a)+(t-a)f'(a)$$
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
$endgroup$
hint
for $t$ close to $a$,
$$f(t)approx f(a)+(t-a)f'(a)$$
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
answered Dec 13 '18 at 19:10
hamam_Abdallahhamam_Abdallah
38.1k21634
38.1k21634
add a comment |
add a comment |
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