Question

The function f(x) is an unshifted exponential function which goes through the points (2,5) and (3,4).

A. what is the equation for f(x)
B. Find f(10) and f(100)

Answer 1

`f(x) = ae {}^(bx) \\ f(2) = 5 \: \: \: \: \: f(3) = 4`

`5 = ae {}^(2b) \: \: \: \: \: \: \: 4 = ae {}^(3b) \\ divide \: both \: systems \\ e {}^(b) = (4)/(5) \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = (125)/(16)`

`f(x) = (125)/(16) e {}^(ln(0.8)x)`

`f(10) = (125)/(16) e {}^(10ln(0.8)) = (65536)/(78125) \approx0.838861 \\ f(100) = (125)/(16) e {}^(100ln(0.8)) = \frac{4 {}^(98) }{5 {}^(97) } \approx1.59 * 10 {}^( - 9)`