paul is comparing two high - speed internet service providers (isps) for his business. the graph represents…

paul is comparing two high - speed internet service providers (isps) for his business. the graph represents the cost of each isp as a function of t, the duration in months of a service contract. if c(t)=180 + 10t represents isp a and c(t)=25t represents isp b, how long would the service contracts need to be for the total costs to be the same? 6 months 8 months 10 months 12 months

paul is comparing two high - speed internet service providers (isps) for his business. the graph represents the cost of each isp as a function of t, the duration in months of a service contract. if c(t)=180 + 10t represents isp a and c(t)=25t represents isp b, how long would the service contracts need to be for the total costs to be the same? 6 months 8 months 10 months 12 months

Answer

Explanation:

Step1: Set the two cost - functions equal

Set $180 + 10t=25t$.

Step2: Isolate the variable t

Subtract $10t$ from both sides: $180=25t - 10t$. Simplify the right - hand side: $180 = 15t$.

Step3: Solve for t

Divide both sides by 15: $t=\frac{180}{15}=12$.

Answer:

12 months