Leo and Vanessa both have a certain amount of money and plan to spend a certain amount each week until they run out. Vanessa starts with $400 and plans to spend $80 every 2 weeks. Leo plans to spend his money half as fast and has the same amount of money as Vanessa after 7 weeks.

Leo started with $260

The balance of Vanessa and Leo after 7 weeks = $120

Step-by-step explanation:

Vanessa started $400

Vanesaa spending rate= $80/2weeks

In a week she would spend=$40/week

In 7 weeks should spend =40*7 = $280

Her balance after 7 weeks is =

$400 - $40 × x

$400 - $280

= $120

Leo spends at half of vanessa’s rate= $20/week

In 7 weeks leo will spend

$20 × x weeks

= 20 × 7 = $140

Since Leo and Vanessa’s balance would be the same after 7 days then leo balance is $120

Hence, the amount Leo started with $120 + $140= $260

In order to confirm your above answer

The Equation can be given as

$400 - $40 ×x = $260 - $20 × x

Where x = 7 weeks

$400 -40x = 260 - 20x

$400 - 40× 7 = $260 - 20× 7

$400 - 280 = $260 - 140

$120 = $120

The population of bacteria can be expressed as a function of number of days.

Population = where n is the number of days since the beginning.

Step-by-step explanation:

Number of bacteria on the first day=

Number of bacteria on the second day =

Number of bacteria on the third day =

Number of bacteria on the fourth day =

As we can see , the number of bacteria on any given day is a function of the number of days n.

This expression can be expressed generally as where n is the number of days since the beginning.