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You can afford monthly deposits of $250 into an account that pays 4.8% compounded
monthly. How long will it be until you have $11,900 to buy a boat?
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Step-by-step explanation:

The formula you need for this is

where

A(t) is the amount after a certain number of years has gone by,

P is the initial deposit,

r is the interest rate in decimal form,

n is the number of compoundings done per year, and

t is the amount of time in years.

For us,

A(t) = 11900

P is 250

r is .048

n is 12 (there are 12 months in a year)

t is our unknown. Filling in:

which simplifies a bit to

. Now we'll divide both sides by 250:

and then take the natural log of both sides to bring that t down out front:

and then

ln(47.6) = 12t ln(1.004). Now divide both sides by ln(1.004) to isolate the 12t:

967.6383216 = 12t and divide both sides by `12 to get

t = 80.6 months which is 6.7 years

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x