A Math question (Calculus)?

Question

An exponential equations has base .8 If f(10)=50, find f(11) Please show the steps . Show me how to do with out calculater

Answer 1

For an exponential with base 0.8,
f(x) = a(0.8)^x

You need to solve first for a.
f(10) = a(0.8)^10
50 = a(0.8)^10
a = 50 / (0.8^10)

Now you can find f(11)
f(11) = a(0.8)^11
f(11) = 50(0.8)^11 / (0.8^10)
f(11) = 50(0.8)
f(11) = 40

Answer 2

Louise gave you a very good answer. Since f(x) = a(0.8)^x, f(10)= a(0.8)^10 and f(11) = a(0.8)^11, which is just f(10) times another 0.8.

So f(11) = 0.8•f(10) = 0.8•50 = 40. Certainly no need to get into logarithms, much less nonstandard ones like base 0.8. Just understand that the essential character of exponential functions is the repeated multiplication by the same factor.

Answer 3

8^(10x)=50
so...solve for x then plug in 11 to get your new answer.

Here's how to solve. Take the log with base 8 of each side.
log8^(10x)= log50. Remeber log with base 8.
10x= log50.
x= (log50)10

Remember...log with base 8. I just can't show it on here. But I hope that helps. :)

Answer 4

y = k * .8^ x

f(10) = 50 = k * .8^10
f(11) = y = k * .8^11

y/50 = (k * .8^11) / (k * .8^10)
y/50 = (.8^11) / (.8^10) = .8^ (11 - 10) = .8^1

y = 50 * .8 = 40