12 divided by the sum of h and 2
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The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.
The expression shown is an <em>exponential expression</em>. An exponential expression usually takes the form , as this one does. A represents the <em>initial value</em>, in this case-the initial number of bacteria. B represents the <em>growth rate</em>. When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion. In this case, a=57, and b=0.31.
Hope this makes sense!
To see how much interest she'll get after a quarter:
$4132.79 + ($4132.79 × 0.048) = $4331.16
After two quarters:
$4331.16 + ($4331.16 × 0.048) = $4359.06
You can keep going until eventually reaching $8000 then see how many quarters has passed. That's a lot of calculator work!
There's another way that uses less calculation, but more algebra. I call it the exponential formula method! There's this general formula for stuff that increases exponentially, like virus, population, and MONEY:
M is money, d is deposit, t is time taken, and c is just some unknown constant related to the interest rate. There's also the natural logarithm form of this equation, which will come in handy later:
Alright first we gotta find that constant c for this equation to be useful! Let's plug in stuff we know.
We know how much she'll have after one quarter (0.25 years), and we know how much she deposited initially.
After pressing some buttons on the calculator we'll find that c = 0.1875.
Great! Now we can use that formula to find how many years (t) it'll take to reach M=$8000. To save time I'm going to use the natural log form:
That will give us t = 3.522 which means it'll take approximately 3.5 years for her deposit to reach $8000!
$4132.79 + ($4132.79 × 0.048) = $4331.16
After two quarters:
$4331.16 + ($4331.16 × 0.048) = $4359.06
You can keep going until eventually reaching $8000 then see how many quarters has passed. That's a lot of calculator work!
There's another way that uses less calculation, but more algebra. I call it the exponential formula method! There's this general formula for stuff that increases exponentially, like virus, population, and MONEY:
M is money, d is deposit, t is time taken, and c is just some unknown constant related to the interest rate. There's also the natural logarithm form of this equation, which will come in handy later:
Alright first we gotta find that constant c for this equation to be useful! Let's plug in stuff we know.
We know how much she'll have after one quarter (0.25 years), and we know how much she deposited initially.
After pressing some buttons on the calculator we'll find that c = 0.1875.
Great! Now we can use that formula to find how many years (t) it'll take to reach M=$8000. To save time I'm going to use the natural log form:
That will give us t = 3.522 which means it'll take approximately 3.5 years for her deposit to reach $8000!