Suppose a developer is interested in building a new apartment community. through her market research, the developer has determined that the target market segment potential in year 1 consists of 100 households. the developer believes that the target market segment potential will grow by 5% annually over the next five years. if the developer projects a capture rate of 25% for each of the next five years but is only to sell 26 apartment units in each of the next five years, in which year will her actual sales first fail to meet her projected sales numbers?

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (a) find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) suppose that the rising fuel costs increase the utility's variable costs from $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?