Respuesta :
Step-by-step explanation:
We can use exponential interpolation to find the value of f(5) based on the given values of f(4.5) and f(5.5).
Let f(x) = a*b^x, where a and b are constants to be determined.
Using the given values, we have:
9 = a*b^4.5
46 = a*b^5.5
Dividing the second equation by the first, we get:
46/9 = b^1
Taking the logarithm of both sides, we get:
ln(46/9) = ln(b)
Solving for b, we get:
b ≈ 2.178
Substituting this value of b into the first equation, we get:
9 = a*2.178^4.5
Solving for a, we get:
a ≈ 0.000468
Therefore, f(x) ≈ 0.000468*2.178^x
Thus, f(5) ≈ 0.000468*2.178^5 ≈ 2.95
Therefore, f(5) is approximately equal to 2.95 to the nearest hundredth.
