4 Solar Tech EcoTech Inc. is a company specializing in environmentally friendly technologies and have recently created a more efficient and light weight solar panel. Like all technologies, these solar panels are prone to failure and need to be repaired over time. The time until a solar panel fails is exponentially distributed with a mean of 10 years. (a) Calculate the probability that a new solar panel will fail within 5 years of installation. (b) Given that a solar panel has already functioned for 7 years without failure, calculate the probability that it will fail within the next 3 years. (c) Suppose EcoTech provides a warranty and promises they will repair the solar panels the first 7 times they fail. What is the likelihood a warranty will end in 100 to 120 years? (d) EcoTech Inc. decides to further their environmental impact by planting trees for every solar panel they sell. EcoTech Inc. aims to ensure that at least 100 trees reach maturity. acknowledging that the survival rate of newly planted trees is 75%, Calculate the probability that EcoTech Inc. will need to plant more than 130 trees to achieve their goal of 100 mature trees.