1. ## Exponential growth/decay

1. I just want to know if this equation is correct

The # of bacteria growing in meat doubles each day while in a fridge. When you buy the meat, it contains 300 bacteria. Find a function that represents the # of bacteria in the meat after t days

2. If an inflation rate remains at 4% a year, then the amount a dollar is worth decreases by 4% a year
a) assume today a dollar is actually worth $1, at the stated rate of inflation, how much will this dollar be worth after 6 years b) find a function which describes the value of a dollar after t years I tried and made a function f(t) = 1 - (1/25)^t but it didnt work 3. A yeast colony is growing exponentially. It starts with 400 individuals and 2 hours later it has 4,000. Find a function describing the amount of yeast in the colony after t hours 2. Hi realintegerz, 1.The # of bacteria growing in meat doubles each day while in a fridge. When you buy the meat, it contains 300 bacteria. Find a function that represents the # of bacteria in the meat after t days It is an exponential function, so it will have the form$\displaystyle y=ab^t$, where$\displaystyle a$is the initial value and$\displaystyle b = 1+r$with$\displaystyle r$being the growth rate. Now see if you can put them together. 2. If an inflation rate remains at 4% a year, then the amount a dollar is worth decreases by 4% a year a) assume today a dollar is actually worth$1, at the stated rate of inflation, how much will this dollar be worth after 6 years
b) find a function which describes the value of a dollar after t years

I tried and made a function f(t) = 1 - (1/25)^t but it didnt work
Similar to #1, $\displaystyle y=ab^t$ is what you need. In this case your growth rate (or decay rate) "$\displaystyle r$" is going to be negetive, in particular, $\displaystyle r=-.04$.

3. A yeast colony is growing exponentially. It starts with 400 individuals and 2 hours later it has 4,000. Find a function describing the amount of yeast in the colony after t hours
Same idea here. You need to find a formula, $\displaystyle y=ab^t$. The information above gives two points $\displaystyle (0, 400)$ and $\displaystyle (2, 4000)$. You can form two equations by plugging in the points and solve $\displaystyle a$ and $\displaystyle b$.