Find approximate values of the following : `2^(3.02)`

Explanation

Let `y = 2^x`
Then `dy = 2^x Iog 2 dx`
`rArr deltay = 2^x Iog 2 deltax`
` 2^(x+deltax) - 2^x = 2^x` Iog `2 deltax`
`rArr 2^(x+deltax) = 2^x + 2^x` Iog `2 deltax`
Then `2^(3.02) = 2^3 + 2^3` Iog 2 x 0.02 = 8 + 8 x0.3010 x 0.02 = 8+0.04816=8.04816`