Final answer:
To solve compound interest equations for t, divide or multiply both sides of the equation to isolate the exponent, take the logarithm base of the interest rate, and solve for t by dividing the left side by the right side.
Step-by-step explanation:
a. To solve the compound interest equation (5490 = 4800(1.009)) for t, we can use logarithms. First, divide both sides of the equation by 4800 to isolate the exponent: 5490/4800 = 1.009^t. Then, take the logarithm base 1.009 of both sides: log(5490/4800) = t*log(1.009). Finally, divide the left side by the right side to solve for t: t = log(5490/4800)/log(1.009).
b. Following the same steps as in part a, we find that t = log(3900/3000)/log(1.006).
c. To solve the equation (1460 = 1000(1.0015)^(-21)), we can take the logarithm base 1.0015 of both sides and use the negative exponent as an argument: log(1460/1000) = -21*log(1.0015). Divide the left side by the right side to solve for t: t = log(1460/1000)/-log(1.0015).
d.Similarly, solving (5951.70 = 5000(1.00875)^t) for t gives t = log(5951.70/5000)/log(1.00875).
e. The equation (33,010.20 = 30,000(1.008)) can be solved for t by dividing both sides by 30,000 and then taking the logarithm base 1.008 of both sides: log(33,010.20/30,000) = t*log(1.008). Finally, divide the left side by the right side to find t: t = log(33,010.20/30,000)/log(1.008).