Estimate the value of 3 to the power of 2.2 using linear interpolation.
I already answered this question.
MATH - Bosnian today at 9:23pm
in case you forgot,
since 2.2 is 1/5 of the way from 2 to 3,
3^2.2 is 1/5 of the way from 3^2 to 3^3
To estimate the value of 3 to the power of 2.2 using linear interpolation, we need to find the values of 3 raised to powers slightly above and below 2.2 and then interpolate between them.
First, calculate 3 raised to 2:
3^2 = 9
Next, calculate 3 raised to 3:
3^3 = 27
Now, we can interpolate between these two values using the following formula:
Interpolated value = lower value + (difference between values) * (fractional part of the exponent)
In this case, the lower value is 9 and the higher value is 27, and the fractional part of the exponent (0.2) is the decimal part of 2.2.
So, the interpolated value is:
Interpolated value = 9 + (27 - 9) * 0.2
= 9 + 18 * 0.2
= 9 + 3.6
= 12.6
Therefore, the estimated value of 3 raised to the power of 2.2 using linear interpolation is approximately 12.6.