1. **Stating the problem:** We have a company's digital assets valued at 120 million in 2010, growing according to the unlimited growth model: $$V = 120 e^{0.08t}$$ where $t$ is the number of years after 2010. We need to find: a) The value of the assets in 2020. b) The time $t$ when the value reaches 500 million. 2. **Formula and explanation:** The unlimited growth formula is: $$V = V_0 e^{kt}$$ where $V_0$ is the initial value, $k$ is the growth rate, and $t$ is time. 3. **Part (a): Find value in 2020** Since 2020 is 10 years after 2010, $t=10$. Calculate: $$V = 120 e^{0.08 \times 10} = 120 e^{0.8}$$ Using $e^{0.8} \approx 2.22554$, $$V \approx 120 \times 2.22554 = 267.065$$ So, the value in 2020 is approximately 267.07 million. 4. **Part (b): Find $t$ when $V=500$** Set: $$500 = 120 e^{0.08t}$$ Divide both sides by 120: $$\frac{500}{120} = e^{0.08t}$$ Simplify: $$4.1667 = e^{0.08t}$$ Take natural logarithm on both sides: $$\ln(4.1667) = 0.08t$$ Calculate $\ln(4.1667) \approx 1.4271$, So: $$t = \frac{1.4271}{0.08} = 17.83875$$ Therefore, the value reaches 500 million approximately 17.84 years after 2010, i.e., around mid-2027. **Final answers:** a) Value in 2020: approximately 267.07 million. b) Time to reach 500 million: approximately 17.84 years after 2010.