Percent strength gain at 14 days

Powers' model gives the strength of concrete in terms of the gel/space ratio $x$:

$$x = \frac{\text{volume of gel}}{\text{volume of gel} + \text{capillary pores}} = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}$$

where $\alpha$ is the degree of hydration and $w/c$ the water-cement ratio by mass. The numbers come from cement of specific gravity about 3.14: 1 g of cement has 0.319 cm$^3$ volume and produces gel of $2.06\times0.319 = 0.657$ cm$^3$ (including gel pores). Compressive strength:

$$f_c = 240\,x^3\ \text{MPa}$$

(240 MPa is the intrinsic strength of the gel; it varies from about 234 to 255 MPa for different cements.) The ratio $x$ does not depend on the mass of cement; the mass is only needed to give volumes.

Reading of the question

The hydration at 28 days is taken as complete ($\alpha_{28} = 1.0$) and at 14 days $\alpha_{14} = 0.9$ (90% of that at 28 days). Cement = 500 g, $w/c = 0.45$ (the mass cancels in the ratio). "Percent strength gain" is the strength at 14 days as a percentage of the 28-day strength.

28 days ($\alpha = 1$)

$$x_{28} = \frac{0.657}{0.319+0.45} = 0.854, \qquad f_{28} = 240\times0.854^3 = 149.7\ \text{MPa}$$

14 days ($\alpha = 0.9$)

$$x_{14} = \frac{0.657\times0.9}{0.319\times0.9+0.45} = \frac{0.5913}{0.7371} = 0.802, \qquad f_{14} = 240\times0.802^3 = 123.9\ \text{MPa}$$ $$\frac{f_{14}}{f_{28}} = \frac{123.9}{149.7}\times100 = 82.8\%$$

Answer: the concrete gains about 82.8% of its 28-day strength at 14 days (123.9 MPa against 149.7 MPa). Note that 90% hydration gives only about 83% strength because of the cubic relation.