Pre-Calc Help Please Find the exponential function f(x)=Ca^x whose graph goes through the points (0,3) and (2,12). Thank you.?
回答 (3)
2017-03-30 12:39 am
✔ 最佳答案
y = f(x) = C a^xWhen x = 0, y = 3 :
3 = C a^0
C = 3
Then, y = f(x) = 3 a^x
When x = 2, y = 12 :
12 = 3 a^2
a^2 = 4
a^2 = 2^2
a = 2
Then, f(x) = 3 * 2^x
2017-03-30 12:49 am
Let f(x) = y
Hence
y = Ca^x
for the point (0,3)
3 = Ca^(0)
NB Anything to the power 'o' equals '1'
Hence
3 = C(1)
C = 3
When C = 3
y = 3a^x
12 = 3(a^2)
a^2 = 12/3 = 4
a^2 = 4
a = +/- 2
Hence the equation becomes
y = 3(2^x)
f(x) = 3(2^x)
Hence
y = Ca^x
for the point (0,3)
3 = Ca^(0)
NB Anything to the power 'o' equals '1'
Hence
3 = C(1)
C = 3
When C = 3
y = 3a^x
12 = 3(a^2)
a^2 = 12/3 = 4
a^2 = 4
a = +/- 2
Hence the equation becomes
y = 3(2^x)
f(x) = 3(2^x)
2017-03-30 12:48 am
f(x) = Ca^x
f(0) = 3 = Ca^0
= C
f(2) = 12 = 3a^2
3a^2 = 12
a^2 = 4
a = ± 2
f(x) = 3*(2)^x, 3*(-2)^x
f(0) = 3 = Ca^0
= C
f(2) = 12 = 3a^2
3a^2 = 12
a^2 = 4
a = ± 2
f(x) = 3*(2)^x, 3*(-2)^x
收錄日期: 2021-05-01 13:10:33
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