Question

price of gas at leor's gas station is 81. 50 perlite ifa customer buys a minimum of 10 litres, a discount of $5 is applied. this can be modelled by the following function. l, which gives the total cost when buying a minimum of 10 litres at leon's gas station. [(2) = 1.502-5, 2≥ 10 where a is the number of litres of gas that a customer buys. .tz1.4 (a) find the total cost of buying 40 litres of gas at leon's gas station. [2] (b) find l- (70). [2) (c) the price of gas at erica's gas station is $1. 30 per litre. a customer must buy a minimum of 10 litres of gas. the total cost at erica's gas station is cheaper than leon's gas station when x > k.

Answer 1

To find the total cost of buying 40 litres of gas at Leon's gas station, use the given function l(a) = 1.50a - 5. The total cost is $70. To find l'(70), differentiate the function l(a) = 1.50a - 5, resulting in l'(a) = 1.50. The value of l'(70) is 1.50.

Step-by-step explanation:

To find the total cost of buying 40 litres of gas at Leon's gas station, we need to use the given function:

l(a) = 1.50a - 5, if a ≥ 10

1. Since we're buying 40 litres of gas, which is greater than 10 litres, we can use the function to find the total cost:
2. l(40) = 1.50(40) - 5
3. l(40) = 75 - 5
4. l(40) = 70
5. The total cost of buying 40 litres of gas at Leon's gas station is $70.
6. To find l'(70), we need to differentiate the function:

l'(a) = 1.50

1. Since l'(a) is a constant, the derivative of the function l(a) = 1.50a - 5 is simply l'(a) = 1.50.
2. Therefore, l'(70) = 1.50

The value of l'(70) is 1.50.

Note: The question mentions the price of gas at Erica's gas station, but it is not relevant to the calculations required.