In economics, the formula relating the future value (F)
and present value (P) at simple interest (i) and number of years (n) is:
F = P (1 + i)^n
Since we are to find for n, let us rewrite this equation:
(1 + i)^n = F / P
Taking the log of both sides:
n log (1 + i) = log (F / P)
n = log (F / P) / log (1 + i)
Substituting the given values:
n = log (2,340 / 1,800) / log (1 + 0.05)
n = log (1.3) / log (1.05)
n = 5.38
<span>Hence it will take Joe around 5.38 years</span>
Answer:
C. Leo scored points in 3/10 of his attempts
Step-by-step explanation:
30% is 30/100
Which can simplify to
3/10
Answer:
Converges for x in (-16,2) and the value of convergence is
Step-by-step explanation:
Recall that a series of the form converges if |r|<1. The value of convergence, when the series converges is
The given series is
So, it converges if and only if
Equivalently, we get
Which is the interval . So the series converges over the interval (-16,-2).
The value of converge for an x in that interval is
.
Answer:
Step-by-step explanation:
Using the rules of exponents
• × =
• =
Given
× , then
= ×
= ×
=
=
Step-by-step explanation:
if we translate (shift) a function g(x) to the right by k to create h(x), then h(x) creates the same functional values as g(x), but they happen now for higher x ("later", if you consider x as a kind of time).
so, e.g.
h(0) = g(0 - k)
or
g(0) = h(0 + k)
and to translate to the left by k has the opposite effect. the original results happen "earlier" on the x-axis.
so, e.g.
h(0) = g(0 + k)
or
g(0) = h(0 - k)
so, all we need to do is to replace every occurrence of x by (x - k) if shifting right, or by (x + k) if shifting left.
our graph is
10x² - 2x + 4y² - 4y = 40
so, translating this 4 units to the right gives us
10(x - 4)² - 2(x - 4) + 4y² - 4y = 40
10(x² - 8x + 16) - 2x + 8 + 4y² - 4y = 40
10x² - 80x + 160 - 2x + 8 + 4y² - 4y = 40
10x² - 82x + 4y² - 4y = -128
translating the original graph 3 units to the left gives us
10(x + 3)² - 2(x + 3) + 4y² - 4y = 40
10(x² + 6x + 9) - 2x - 6 + 4y² - 4y = 40
10x² + 60x + 90 - 2x - 6 + 4y² - 4y = 40
10x² + 58x + 4y² - 4y = -44