Final answer:
The correct statements based on the equation y = 150,000(1.08)^t are that the company's initial earnings are $150,000 and the earnings are projected to increase by 8% annually.
Step-by-step explanation:
The equation y = 150,000(1.08)^t is used for estimating the yearly earnings of a company. Based on this equation:
- A) The company's initial earnings (t=0) are $150,000. When t is 0, the equation simplifies to y = 150,000, which represents the initial earnings of the company.
- B) The earnings are projected to increase by 8% annually. We can tell this because the base of the exponent, 1.08, indicates that each year the earnings multiply by a factor of 1.08, or increase by 8%.
- C) Antonio is the president of the company. This statement is not supported by the given equation and therefore cannot be determined to be accurate.
- D) The company's earnings will remain constant over time. This statement is incorrect, as the equation includes an exponent that increases earnings annually.
- E) The company's earnings will decrease by 8% annually. This is incorrect because the factor 1.08 causes an increase, not a decrease.
In summary, the correct statements based on the provided equation are A and B, as they accurately describe the company's initial earnings and its projected growth rate.