Asked by Becky
The exponential function y(x)=Ce^ax satisfies the conditions y(0)=6 and y(1)=7.
(a) Find the constants C and a. Enter the exact value of a.
(b) Find y(2). Enter the exact answer. Simplify the answer so it does not contain any logarithms.
(a) Find the constants C and a. Enter the exact value of a.
(b) Find y(2). Enter the exact answer. Simplify the answer so it does not contain any logarithms.
Answers
Answered by
Steve
6 = Ce^0
C = 6
7 = 6e^a
a = ln(7/6)
y(x) = 6e^(ln(7/6)x) = 6(e^(ln(7/6)))^x = 6*(7/6)^x
y(2) = 6(7/6)^3 = 343/36
C = 6
7 = 6e^a
a = ln(7/6)
y(x) = 6e^(ln(7/6)x) = 6(e^(ln(7/6)))^x = 6*(7/6)^x
y(2) = 6(7/6)^3 = 343/36
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