The exponential function is
f(x)=ab^x, where b is the base, the number to multiply every time x is increased by 1.
If f(x)=92, f(x+4)=280, then
f(x+4)/f(x) = 280/92 = ab^(x+4)/(ab^x) = b^4
to find the base b,
b^4=(280/92)
b=(280/92)^(1/4) ..... fourth root, or take square-root twice
=3.4035^(1/4)
=1.3208 (accurate to 4 places of decimal).
Edit: 92*1.3208^4 gives 279.9858 (missing little bit because of accuracy).
A slightly better accuracy would be
base = 1.320816698856163
and 92*1.320816698856163^4 would still be 279.9999999999993, but VERY close to 280.
So it all depends on the accuracy you need.
If you need more accuracy, please tell me how many accurate digits you'd like the results.
Here it is:
base = 1.320816698856163713875997666455513013800337299231824403890097792042432005288739246325005446716740
and if you multiply together
92*base^4, you will get 280 accurate to at least 90 digits after the decimal.
I think that should be sufficient for what you need. Recall that these calculations cannot be done or verified on a 10 or 12 digit calculator.
Well, to please you, I have calculated it to 500 digits, don't think that's going to be of much practical use for anybody.
By the way, that's as far as I will do this evening. My eyes are almost closing!
base=1.3208166988561637138759976664555130138003372992318244038900977920424320052887392463250054467167408005624428737585147309981331510076693180633495574937759374668399829195521733208637815593771220504215429477168159456265024711237470736388371979840461777898466419772297172931568429339640964205400234392902077320257671263508487367942846685479533507498695981037274512050120058009244868634949261015429944340565311559486391625531554216085859773912355361847787636892603324966350039688974359584811585283183726532
N=8
x= -19
Let me know if you need to see how to solve it
The point at which the two lines intersect is (4,7).
i know the answer to 1 is 10
Answer:
G:O = 3:10
the ratio of green marbles to orange marbles is 3:10
Step-by-step explanation:
Let G, Y and O represent green, yellow and orange marbles respectively.
Given;
the ratio of green marble to yellow marble is 2 : 5
G:Y = 2:5
G/Y = 2/5
the ratio of yellow arbles to orange marbles is 3 : 4
Y:O = 3:4
Y/O = 3/4
the ratio of green marbles to orange marbles G:O;
G/O = G/Y × Y/O
Substituting the values;
G/O = 2/5 × 3/4
G/O = 3/10
G:O = 3:10
the ratio of green marbles to orange marbles is 3:10
